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DESHLER, Donald David, 1946LEARNING DISABILITY IN THE HIGH SCHOOL STUDENT
AS DEMONSTRATED IN MONITORING OF SELF-GENERATED
AND EXTERNALLY-GENERATED ERRORS.
The University of Arizona, Ph.D., 1974
Education, special
Xerox University Microfilms t
Ann Arbor, Michigan 48106
THIS DISSERTATION HAS BEEN MICROFILMED EXACTLY AS RECEIVED.
LEARNING DISABILITY IN THE HIGH SCHOOL STUDENT
AS DEMONSTRATED IN MONITORING OF
SELF-GENERATED AND EXTERNALLY-GENERATED ERRORS
by
Donald David Deshler
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF SPECIAL EDUCATION
In Partial Fulfillment of the Requirements
For the Degree of
DOCTOR OF PHILOSOPHY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1 9 7 4
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by
entitled
Donald David Deshler
.
LEARNING DISABILITY IN THE HIGH SCHOOL STUDENT AS
DEMONSTRATED IN MONITORING OF SELF-GENERATED AND EXTERNALLY-
GENERATED ERRQRS
be accepted as fulfilling the dissertation requirement of the
degree of
Doctor of Philosophy
jj^o
Dissertation Director
L-n-jy
Date
After inspection of the final copy of the dissertation, the
following members of the Final Examination Committee concur in
its approval and recomnend its acceptance:"''
'/
This approval and acceptance is contingent on the candidate's
adequate performance and defense of this dissertation at the
final oral examination. The inclusion of this sheet bound into
the library copy vf the dissertation is evidence of satisfactory
performance at the final examination.
STATEMENT BY AUTHOR
This
requirements
is deposited
rowers under
dissertation has been submitted in partial fulfillment of
for an advanced degree at The University of Arizona and
in the University Library to be made available to bor­
rules of the Library.
Brief quotations from this dissertation are allowable without
special permission, provided that accurate acknowledgment of source
is made. Requests for permission for extended quotation from or re­
production of this manuscript in whole or in part may be granted by
the head of the major department or the Dean of the Graduate College
when in his judgment the proposed use of the material is in the in­
terests of scholarship. In all other instances, however, permission
must be obtained from the author.
SIGNED:
ACKNOWLEDGMENTS
The writer wishes to express his sincere gratitude to the
members of his doctoral committee, Dr. Corrine Kass, Dr. George Leshin,
Dr. Loyd Wright, Dr. Cecil Rogers, and Dr. Wayne Carroll for their
assistance in his doctoral program and dissertation.
Thanks is also
expressed to the school personnel and students who participated in
this study.
A special note of appreciation is extended to Dr. Corrine Kass,
major advisor, who gave unselfishly of her time, energy, and creative
insight throughout the writer's graduate program.
Dr. William R. Ferrell, Professor of Engineering, served as a
consultant during the entire project and provided invaluable assistance
in the analysis of the results and review of the manuscript.
Finally, the author wishes to gratefully acknowledge his wife,
Carol, for the interest, support, and encouragement she constantly
provided, and to his children, Reed and Jill, whose happiness, love,
and warmth minimized the struggles and trials of a doctoral program
and kept life in proper perspective.
ill
TABLE OF CONTENTS
Page
LIST OF TABLES
vii
LIST OF ILLUSTRATIONS
I.
viii
ABSTRACT
x
STATEMENT OF THE PROBLEM
1
Introduction
Statement of the Problem
Theoretical Context and Review of the Literature ....
Learning Disability—A Unique Handicap
Role of Age-Related Functions
Symptomatic Characteristics of Learning
Disability in the Adolescent
II.
MONITORING DEFICIT
9
15
Role of Monitoring in Performance
Design of the Monitoring Tasks
Task One: Creative Writing Task
Task Two: Editing Task
Task Three: Yes-No Spelling Task
Task Four: Two-Alternative Forced-Choice
Spelling Task
Task Five: Vocabulary Task
Conditions of TAsk Administration
Signal Detection Theory
Data Collection
III.
1
2
2
2
6
15
19
19
20
21
23
24
26
26
30
SAMPLING PROCEDURE
31
Initial Population
Specialist Ratings
Procedure
Results
Test Data
Test Selection
Test Administration
Results
Research Population
.
iv
31
32
32
34
37
37
41
41
55
V
TABLE OF CONTENTS—Continued
Page
IV.
RESULTS
57
Task One: Creative Writing
Scoring Procedure
Results
Task Two: Editing
Scoring Procedures
Results
Discussion
Tasks Three and Four: Spelling
Yes-No Spelling Task
Two-Alternative Forced-Choice (2AFC)
Spelling Task
Task Five: Vocabulary
Scoring Procedure
Results
Summary Discussion
Concluding Statement
V.
SUMMARY AND IMPLICATIONS
Statement of the Problem
Monitoring Deficit
Design of the Monitoring Tasks
Data Collection
Sampling Procedure
Initial Population
Specialist Ratings
Test Data
Research Population
Results
Task One: Creative Writing
Task Two: Editing
Task Three and Four: Spelling
Task Five: Vocabulary
Methodological Implications
Bayesian Statistics
Signal Detection Theory
Concluding Statement
Practical Implications
Implications from Test Data
Implications from Task Data
...
58
58
58
66
66
66
66
73
73
81
84
84
85
88
91
92
92
92
93
93
93
93
94
94
97
97
98
99
99
100
100
100
101
103
103
103
104
APPENDIX A:
QUESTIONNAIRE AND PROCESS OUTLINE
106
APPENDIX B:
SAMPLE SUMMARY SHEET
117
vi
TABLE OF CONTENTS—Continued
Page
APPENDIX C:
RAW TEST SCORE DATA
119
APPENDIX D: m AND n VALUES
122
APPENDIX E:
LIKELIHOOD RATIOS FOR EACH SUBJECT
123
APPENDIX F:
RAW TASK DATA
128
APPENDIX G: d' VALUES FOR TASKS THREE AND FOUR:
SPELLING
134
APPENDIX H: p(e) VALUES FOR TASK THREE:
SPELLING (YES-NO)
136
REFERENCES .....
138
LIST OF TABLES
Table
Page
1.
LD group sample selection data
35
2.
NLD group sample selection data
36
3.
Posterior probability of learning disability for
each student in the learning disability and nonlearning disability groups, given eight sets of
scores
49
Posterior probabilities for the learning disability
group based on sequential addition of test data
54
Learning disability and non-learning disability
samples as defined by number, age, age range,
and grade range
56
Comparison of variances and means of learning
disability and non-learning disability groups
for Task One, Creative Writing
59
Comparison of variances and means of learning
disability and non-learning disability groups
for Task Two: Editing
67
4.
5.
6.
7.
vii
LIST OF ILLUSTRATIONS
Figure
Page
1.
Editing Task passage
21
2.
Yes-No Spelling Task
22
3.
Two-Alternative Forced-Choice Spelling Task
24
4.
Vocabulary Task
25
5.
Hypothetical noise and signal plus noise
distributions
30
Beta distributions for reading comprehension—
Peabody Individual Achievement Test
44
Beta distributions for abstract-concrete—
Picture Story Language Test
44
Beta distributions for blending—Stanford
Diagnostic Reading Test
45
Beta distributions for Mathematics—Peabody
Individual Achievement Test
45
Beta distributions for syntax—Picture Story
Language Test
46
Beta distributions for sentences—Picture
Story Language Test
46
Beta distrlbutions for words—Picture Story
Language Test
47
Beta distributions for words/sentence—
Picture Story Language Test
47
Errors and errors detected by the non-learning
disability group in the Creative Writing Task
60
Errors and error# detected by the learning
disability group in the Creative Writing Task
61
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
viii
ix
LIST OF ILLUSTRATIONS—Continued
Figure
16.
17.
18.
19.
20.
21.
Page
Number of nonerrors detected by learning
disability and non-learning disability
students in the Creative Writing Task
62
Number of errors detected by learning
disability and non-learning disability
students in the Editing Task
68
Number of nonerrors detected by learning
disability and non-learning disability
students in the Editing Task
69
Number of errors corrected by learning
disability and non-learning disability
students in the Editing Task
70
Scatter-plot of p(e|E) and p(e|C) for learning
disability and non-learning disability groups
for the Yes-No Spelling Task
79
ROC Curves for learning disability and nonlearning disability groups for the Vocabulary
Task
86
ABSTRACT
Statement of the Problem
This study attempted to differentiate between learning dis­
ability and non-learning disability in the adolescent by investigating
some characteristics which relate specifically to learning disability
at the high school level.
Identification of learning disability at
the high school level was tested through a Bayesian approach to psycho­
metric test data and through a comparison of the performance of
learning disability and non-learning disability students on selected
tasks.
Monitoring Deficit
A monitoring deficit was studied as a characteristic which
would differentiate between learning disability and non-learning
disability in the adolescent.
It was defined as an impairment in the
student's ability to detect self-generated and externally-generated
errors.
Five school-related tasks, requiring the monitoring of
self-generated and externally-generated errors, were designed to dis­
cover whether a monitoring deficit would be a good indicator of
learning disability.
The task data collected were submitted to
statistical treatments and to analysis by signal detection theory.
x
xi
Sampling Procedure
The research population was systematically refined through the
following steps: (1) Teachers submitted names of students who were
having difficulty in meeting academic standards and the names of those
who were not evidencing learning difficulties; (2) Specialists ratings,
based on available cumulative folder data, were used to select a
learning disability group of 36 students and a non-learning disability
group of 36 students from the initial population; (3) Four tests that
yielded eight sets of scores were selected and administered to measure
a set of component disabilities.
Bayes' theorem was used to determine
the probability that learning disability was present for each student.
Ninety-four percent of the sample identified by the specialists was
classified as learning disability when a cut-off point of .74 was
established.
Results
Five school-related tasks were administered to both groups of
students and scored to determine if the groups could be differentiated
on a variety of error measures.
1.
The results indicated that:
On the Creative Writing Task, significant differences were
found between the variances and means on the measures of errors,
errors detected, percent errors detected, and non-errors
detected for the learning disability and the non-learning
disability groups.
2.
On the Editing Task, significant differences were found be­
tween the means and variances on the measures of errors detected,
xii
percent errors detected, non-errors detected, and percent
errors corrected for the learning disability and the nonlearning disability groups.
No significant difference was
found on errors corrected.
3.
On the Yes-No Spelling Task, a significant difference was found
between the two groups in detectibility of errors.
Detectibility
of the learning disability group was not much better than chance.
A measure of the proportion of error responses for the two
groups showed no significant difference.
The internal consis­
tency of the signal detection model on yes-no data was demon­
strated through its application to the Two Alternative Forced
Choice Spelling Task.
4.
On the Vocabulary Task, a significant difference was found
between the two groups on their detectibility of errors in
vocabulary usage.
The detectibility evidenced by the learning
disability group on this task, however, was considerably
better than their detectibility of errors on the spelling tasks.
This difference in performance may be explained by a welldocumented characteristic of the learning disability group,
namely, that of normal intelligence.
CHAPTER I
STATEMENT OF THE PROBLEM
Introduction
In recent years, demands for remedial services for students
with learning disability have increased significantly due to heightened
awareness of the handicap and subsequent legislation mandating special
education services for all school-age children.
Before appropriate
treatment can be specified for any handicapped population, the issue
of differentiating between those who belong to that target population
and those who do not must be considered.
The major emphasis of resources and research In handicaps
has tended to focus at the young ages.
Even where older children
are served in remedial programs, the materials and methods tend to be
selected from the curriculum for the young child.
Merely treating the
adolescent as if he were the age at which he scores on a particular
test does not take account of developmental factors such as rapid
physical growth and change, emotionality, and peer interactions.
Learning disability is characterized by a persistence or chronicity
which manifests itself in different ways as the child grows and the
school demands change (Haring, 1969, p. 27).
Kass (1973), in.re­
defining learning disability, has suggested that one of the conditions
of the handicap is that it "remains at maturity."
1
2
Statement of the Problem
This study attempted to differentiate between learning dis­
ability and non-learning disability in the adolescent by investigating
some characteristics which relate specifically to learning disability
at the high school level.
Identification of learning disability at the
high school level was tested through a Bayesian approach to psycho­
metric test data and through a comparison of the performance of learning
disability and non-learning disability students on selected high school
tasks.
If a procedure for efficient and effective identification could
be designed on the basis of distinguishing characteristics, the need
for costly expenditures in terms of personnel, time, and financial
resources at the identification stage would be reduced.
Theoretical Context and Review of the Literature
The context in which this study had its genesis involved cer­
tain theoretical postulates: (1) that learning disability is a unique
handicap which is qualitatively different from non-learning disability,
(2) that understanding of the handicap is aided by systematic analysis
of the role of age-related functions, and (3) that certain character­
istics are symptomatic of the handicap at high school age.
A discussion,
including relevant literature, of each of the postulates is provided
below.
Learning Disability—A Unique Handicap
It is assumed that learning disability is a unique handicap
that is qualitatively different from non-learning disability.
3
Measurement and analysis of qualitative differences is difficult,
particularly when dealing with a complex condition like learning
disability. The presence of any factor by itself Is neither sufficient
nor necessary to determine that a child has learning disability.
Many
theoretical and programmatic approaches in special education rest on
the assumption that both general and specific abilities are distributed
normally throughout the population.
As a result, the normal curve is
widely used as a framework for operationally defining deviancy.
Critical to the question of identification and operational
definitions of handicaps is the issue of cut-off points.
Cut-off
points on some general characteristic, such as intelligence, visual
or auditory acuity, have defined mental retardation, blindness, and
deafness as handicaps.
The difficulty with cut-off points has been
well documented in situations of misclasslfication.
In the case of
learning disability, if a cut-off point (from a single score or measure)
could be established, it would not be sufficient to explain the con­
dition because the characteristic would also be present in part of
the non-learning disability group as well.
Thus, describing or
explaining differences between two populations appears to be much
aore complex than the "either-or" solution implied by considering the
condition of learning disability to be located at the lower portion
of a learning continuum as defined by a single cut-off point.
Understanding and clarification of distinctions between
learning disability and non-learning disability can be enhanced by
first observing obvious qualitative differences.
To make qualitative
4
assessments, at this stage of the field's development, attention
might well be focused on extremes in a population.
In this discussion of self-actualization, Maslow (1971)
justifies the study of extremes in a population to explain a particular
phenomenon.
If we want to answer the question how tall can the human
species grow, then obviously it is well to pick the ones who
are already the tallest and study them. If we want to know
how fast a human being can run then it is no use to average
out the speed of a "good sample" of the population; it is far
better to collect Olympic gold medal winners and see how well
they do. If we want to know the possibilities for spiritual
growth, value growth or moral development in human beings,
then I maintain that we can learn most by studying our most
moral, ethical or saintly people (p. 7).
Nichols (1948) conducted a study to identify good and bad
listening habits.
In his analysis of the data he looked at the
extremes (that is, the worst and the best listeners) to form conclusions
about listening.
The massive longitudinal study on the gifted conducted by
Terman (1925-1959) and his associates was based on data gathered from
1500 children whose IQ'6 averaged 150 or higher.
Participants in a Seminar of Scholars at the University of
Arizona (Bryant and Kass, 1972, pp. 74-75) voiced concern over the
fact that many service arrangements and research studies were designed
for children with minor problems as opposed to more severe disabilities
in learning.
It was suggested that such an approach leads to inconclusive
research findings and "uatered down" services to children.
5
The following literature emphasizes the qualitative differences
found in handicapping conditions:
Myklebust (1971) points out that
learning patterns and types of disability are closely associated.
Although the psychology of similarity is relevant, for educational
implications, it is the psychology of differences which is basic to
understanding the cognitive disturbances in exceptional children. "The
question is not whether they (learning disabled) have the capacity for
better achievement but how the disability has affected learning and
cognitive processes" (p. 223).
Hermann (1959) speaks of qualitative differences in the state­
ment, "The large variations in the age at which reading matures are a
manifestation of the fact that a certain number of children differ
qualitatively from the rest in this respect, and must be regarded as
word-blind" (p. 31).
Menyuk (1972) has questioned the assumption that children with
so called "infantile speech" demonstrate delayed language acquisition.
In addition to a delay in language acquisition, she also notes distinct
differences in language behavior.
For example, the performance of the
child acquiring language normally 1B not random and inconsistent as
he goes from one developmental stage to another, whereas language
behavior of language disordered children JL_s inconsistent and random.
Johnson (in Bryant and Kasa, 1972, p. 142) reported similar
findings in her study of the issue of delay versus disability in lan­
guage acquisition.
Using norms for scoring developmental types in
young children, she found that children with specific language disorders
6
showed some unusual patterns.
For example, they were found to use few
designators and they evidenced particular difficulty with negation and
question forms.
Deutsch and Schumer (1970) note that an evaluation of behavior
of the brain-injured child should rest on developmental considerations—
not only in contrast to normal controls, but also to developmental
characteristics of the brain-injured population itself.
This suggests
the notion of a unique developmental pattern of deviancy as opposed
to a developmental pattern of normalcy.
Qualitative differences are specifically mentioned by Strother
in the Seminar of Scholars (Bryant and Kass, 1972) in the following
statement:
... taking a seven or eight year old and looking at his
performance on a draw-a-man test or his performance in sen­
tence production and you find that this is not really an
immature performance but that it's qualitatively different
than the performance of other children ... if you lose
the function of some muscles in the leg, other muscles
hypertrophy and your whole muscular system in ambulation
functions differently than it did before. So maybe, if
there is a functional deficiency early, we see a different
kind of development in the rest of the cognitive system
(p. 144).
For the purpose of this study, therefore, efforts were made to
sample only those individuals representing extremes in disability with
particular emphasis on qualitative differences.
Role of Age-Related Functions
A second assumption is that disability at the high school level
is characterized by a lack of hierarchical acquisition of functions
7
associated with normal achievement.
Basic to considering the problem
of Identification of a population is the Issue of Isolating or de­
fining the functlon(s) which would be most closely related to the
disability at a given age level.
Ausubel and Ausubel (1971) speak of the cumulation of evidence
suggesting that intellectual ability becomes more differentiated as
well as integrated in adolescence:
This trend exists despite the fact that the older individual
who has presumably undergone the shift from concrete to ab­
stract logical operations in more subject matter areas, is
probably more homogeneous in his mode of cognitive functioning.
Increased integration occurs within the various component
8ubabilities (p. 44).
Lurla (1966) believes that higher mental functions are widely
represented throughout the cortex as systems of functional combination
centers.
He also concludes that higher mental functions are neither
preformed nor do they mature independently, but are formed in the
process of social contact and objective activity which gradually
acquire complex connections.
During the early stages of development,
the sensory and motor basis for learning is very important, but during
the later stages of development, the higher mental functions develop
more complex systems of connections.
Hunt (1961) speaks of the hierarchical acquisition of functions
in the statement:
A conception of intelligence as a problem-solving capacity
based on a hierarchical organization of symbolic representations
and information-processing strategies deriving to a considerable
degree from past experience, has been emerging from several
sources. These sources include observations of human behavior
in solving problems, the programming of electronic computers,
and neuropsychology (p. 109).
8
Hebb's (1949) neurophysiological theory of cell assemblies
also emphasizes successive integration.
The gradual integration of
cell assemblies into more complex sequences results in the continued
development of higher order cerebral organization and hence cognitive
growth.
In the preface to his study entitled, The Adolescent Spurt in
Mental Growth Bengt-Olov Ljung (1965) cautions against the danger of
oversimplifying mental development exclusively in terms of a single
sweeping principle, such as increasing differentiation or increasing
integration.
While Ljung's caution is well taken, the need to study a
breakdown in learning in relation to the complexity of developmental
functions is still warranted.
Birch and Belmont (1964, 1965), Birch and Bitterman (1951),
and Birch and Lefford (1963) noted the emergence of age-specific
curves of growth for different sets of intersensory systems in normal
populations and found them to be "delayed" in brain damaged children.
They suggest that this restricts their potential for the normal
utilization and Integration of environmental Information.
Deutsch and Schumer (1970) found that brain-injured subjects,
when presented with intersensory stimuli, have difficulty integrating
and responding to the information.
They were found to perform on
levels equal to those of comparable intact groups provided simple,
unimodal tasks were used; as task complexity or involvement of inter­
sensory functions increased, behavioral deficits became more pronounced.
9
Kass (1969), in a review of research in learning disabilities,
stresses the important role of age-related factors in both diagnosis
and remediation of learning disabilities.
She concluded that charac­
teristics which are ascribed to learning disability at one age are not
always the same at another age.
The age-related process which was considered in this study was
the Integration process, as defined in Wissink (1972): "The process
by which separately learned components from the processes of sensory
orientation, memory, reception, and expression are unified and compacted
into one internal representation or gestalt (the whole is more than
the sum of its parts)"(p. 86).
suggested for this study:
Another way of defining Integration is
"the process by which previous learning is
Integrated into habitual modes of responses."
This process probably
begins around nine years of age.
By the time a student reaches high school age, the process of
Integration should be developed to such a degree that the individual
is capable of performing in a highly efficient manner on complex tasks.
When basic skills have not been acquired by high school age, performance
in curriculum requirements will be affected since the academic materials
at this level are complex in nature and demand the application of skills
in an efficiently synthesized manner.
Symptomatic Characteristics of Learning
Disability in the Adolescent
A third assumption was that certain characteristics are symp­
tomatic of the handicap at the high school age.
Traditionally,
correlational techniques have been used to diucover factors related
10
to learning disability.
These techniques, however, have not been
completely satisfactory.
DeRuiter (1973) notes the following limitations
of correlational studies:
(1) they do not account for all of the factors which are
important, (2) they do not clearly define the relative im­
portance of the factors, (3) they do not specify a set of
factors which can be used to determine that a learning dis­
ability is present, and (4) they give little information
about the degree of certainty or the probability that
learning disability has been accuratcly identified (p. 14).
A relatively new application of Bayesian statistics to research
on identification of characteristics peculiar to learning disability
has been implemented at The University of Arizona since 1971.
A num­
ber of doctoral dissertations (Wissink, 1972; DeRuiter, 1973; Johnson,
1973; Kaiser, 1974) have demonstrated the viability of the method.
Professor William R. Ferrell of the Systems and Industrial Engineering
Department at The University of Arizona has provided methodological
consultation for this research.
A joint effort between special
education and systems and industrial engineering aeeas to have over­
come one research difficulty stated by HcHanvara (1973) in the following:
One difficulty that is generally recognized as a signifi­
cant factor contributing to the gap between Che development
of optimization (decision) models ami their application to
educational decision making is the serious Inability of edu­
cators and operations research analysts to effectively
consunlcate with each other (p. 29).
Extensive explanations of Bayesian statistics nay be found in
Edwards, Llndfsan and Savage (1963), Stllson (1966), Cornfield (1969),
Wood (1972), and Sheridan and Ferrell (In press).
Basically, bayesian
statistics provided a Beans of quantitatively expressing "the way In
11
which prior convictions about the state of the world are revised on
the receipt of new evidence" (Wood, 1972, p. 630).
A key idea is
"that probability is orderly opinion, and that inference from data is
nothing other than the revision of such opinion in the light of
relevant new information" (Edwards, Lindman and Savage, 1963, p. 194).
In the field of learning disability, Bayesian statistical
techniques can be used to (1) deal with information about learning
disability in the absence of completely definitive information about
the factors that comprise this condition, (2) revise and update sub­
jective opinion about learning disability children as psychometric
data becomes available, and (3) combine probabilistic information about
the factors that are important in learning disability in a sequential
fashion to yield a probability that learning disability has been
identified.
Because Bayesian statistics have these capabilities, they
appear to provide a potentially powerful means of analyzing the data
collected in this study.
The initial attempt to discover deficits or characteristics
most closely related to learning disability was made by Wissink (1972).
Ulssink investigated the application of Bayesian methodology to the
special education problem of identification of children with learning
disability.
The condition of learning disability was considered a
cooplex handicapping condition composed of component disabilities,
8one or all of which may combine to affect efficiency In learning.
Wlsulnk's search of the literature revealed a list of over 100 charac­
teristics reported to be associated with learning disability.
Because
12
these were overlapping, Incompletely defined, not organized, and
expressed In Inconsistent language, the characteristics were combined
Into 40 component disabilities.
These were defined and arranged
within an outline of five psychoeducatlonal processes: (1) sensory
orientation, (2) memory, (3) reception, (4) expression, and (5) Inte­
gration.
The outline was sent to specialists in learning disability
for probability estimates which could be submitted to Bayesian
analysis.
The entire Wissink questionnaire is provided in
Appendix A.
Each specialist in Wlssink's sample was asked to estimate
(1) the percentage of the children having each component disability
in the learning disability population, (2) the percentage of the
children having each component disability In the non-learning disability
population, and (3) the percentage of learning disability children in
the total school population.
A straightforward application of "Bayesian revision of sub­
jective probabilities" to the percentage estimates of the specialists
yielded a small number of discriminating component disabilities.
The
five most discrinitiating component disabilities for the identification
of learning disability were:
attention deficit, auditory-visual
coordination deficit, visualization deficit, auditory speed of
perception deficit, and listening comprehension deficit.
The processes
of Sensory Orientation and Integration contained component disabilities
which were the most effective identifiers.
13
For purposes of this study, only the component disabilities
defined under Integration were considered. Appendix A shows these
to be visualization, sound blending, prediction, monitoring, visual
speed of perception, and auditory speed of perception deficits.
Two
of the most discriminating component disabilities in the Wissink study
(1972) were visualization and auditory speed of perception.
DeRuiter (1973) found tests for the component disabilities
judged by the Wissink sample (1972) to be highly diagnostic (17 sets
of scores) and administered these to two groups of children aged seven
through 12.
One group consisted of 25 children with learning disability,
and the other group consisted of 25 children without learning disability.
Bayesian techniques were applied to the psychometric data, and the four
tests which discriminated most effectively between learning disability
and non-learning disability were:
(1) Picture Story Language Test
(Myklebust, 1965), a measure of the writing component disability;
(2) the Monroe Visualization Test, Word score (Monroe, n.d.), a measure
of the visualization component; (3) the Monroe Word Discrimination
Test (Monroe, 1932), a measure of the monitoring component; and
(A) the Gate8-MacGinitie Reading Comprehension test (Gates and
MacGinitie, 1965), a measure of the reading comprehension component.
Visualization and monitoring are component disabilities defined under
the Integration process.
Combining the most discriminating component disabilities of
the Integration process from both the Wissink (1972) and the DeRuiter
(1973) studies reveals that monitoring, visualization, and auditory
speed of perception are of Interest for studying learning disability
in the high school student.
Correlations done by DeRuiter on test
data showed that scores for monitoring and visualization correlated
.76, scores for monitoring and auditory speed of perception correlated
.82, and scores for visualization and auditory speed of perception
correlated .68.
It was concluded, therefore, that those components
were not independent even though they were defined as such.
Only the
component disability of monitoring was examined in this study.
A monitoring deficit is defined as an impairment in the child's
ability to detect self-generated or externally-generated errors.
Wissink (1972) found that learning disability specialists estimate
that a monitoring deficit occurs in a learning disability population
three times as often as in a non-learning disability population.
CHAPTER II
MONITORING DEFICIT
This chapter will discuss (1) the role of monitoring in
performance, (2) the design of the monitoring tasks, (3) the methodo­
logical tool of signal detection theory, and (4) the data collection.
Role of Monitoring in Performance
The role of monitoring, or the detection of errors in per­
formance, is a crucial one in both learning and performance.
To learn
a skilled, highly integrated response and to perform in a "competent,
accurate, rapid and expert fashion" (Welford, 1968, p. 12), one must
attend and respond to feedback data generated by his own response or
by external information.
The important role that feedback plays in
learning and performance has been emphasized in the psychological
literature.
Some selected references are cited below.
Powers (1973) has proposed a model of behavior where error
information and feedback are the basic components.
Powers maintains
that all behavior is oriented around the control of certain error
quantities through the use of feedback information.
Error is defined
as the difference between a condition of the situation as the subject
sees it, and a reference condition as he understands it.
A subject
will respond to an error to reduce it, correcting it with respect to
a reference condition.
Therefore, internal reference conditions and
15
16
situations as perceived by the organism, not environmental situations,
lead to responses.
Of feedback Powers concludes:
. . when correctly
analyzed, feedback is the central and determining factor in all
observed behavior" (p. 44).
Elwell and Grindley (1938) made the perceptive observation
that human subjects do not repeat rewarded responses, as animals seem
to do.
errors.
Rather, on a second trial, the human attempts to correct his
An unsuccessful movement results in a variation in the
response just made, not its repetition.
This assessment is unlike
the Thorndikian S-R interpretation which requires a repetition of
rewarded responses and avoidance of punished ones but no accounting
for improvement in performance based on systematic correction of
errors.
Adams (1971) also discusses the absence of provisions for
error detection and correction as a shortcoming of the Thorndikian
Law of Effect in the following statement:
What kind of theoretical status should we give KR
(knowledge of results or feedback)? The position taken
here is that KR is foremost a source of information which
results in corrections that eventually lead S to a correct
response, rather than an automatic reward effect as
Thorndlke and those in his tradition would have it (p. 122).
Bilodeau (1961) sumnwrized the Important role of feedback
in the statement"
"Studies of feedback or knowledge of results . . .
show it to be the strongest, most important variable controlling
performance and learning . .
(p. 255).
Bilodeau supports this
position by pointing out the effect on performance of eliminating
feedback information.
For example, the removal or displacement in
17
time or space of visual feedback from handwriting or driving tasks
was found to have marked negative effects on performance.
Smith and Sussman (1969) speak of the significant role of
sensory feedback in motor learning:
"motor learning has been found
to be absent in learning tasks in which dependable feedback guidance
of movement fails to occur and to be present in comparable tasks
in which immediate sensory feedback occurs" (p. 137).
While the literature on the related topics of error detection,
performance, feedback, and vigilance collected by psychology is
extensive, Halcomb and Blackwell (1969) found that the use of vigilance
tasks in studying the parameters of specific populations was sparce.
In their review for the U.S. Army Engineering Laboratories only six
of 728 reported vigilance studies were concerned with special groups,
i.e., brain damaged and mentally retarded.
Out of four of the more
widely-used textbooks in learning disability and special education,
only one (Myers and Hammill, 1969) speaks of the role of feedback in
learning, and then only cursorily.
A re-emphasis in this area seems warranted.
Adams (1971)
pointed out the need for "new thinking about errors and huisan capacity
to detect and correct theta.
All of our learning theories treat error*
lncldently . . . the sensing and using of error information is not a
central feature of behavior for our contemporary theories, which neauo
that they are open-loop, not closed-loop" (p. 116).
An open-loop
system has no feedback or mechanism for error regulation; the input
events exert their influence, the system effects its crauaforn*tio«
on the input, and the syscea has an output.
A closed-loop t>y*teat, oo
18
the other hand, has feedback, error detection and error correction as
key elements.
An Internal reference specifies the desired value for
the system, and the output of the system is fed back and compared to
the reference for error detection, and if necessary, corrected.
Much research conducted in the use of feedback information
(knowledge of results) is carried out in psychological laboratories.
Laboratory settings provide conditions in which independent variables
are manipulated experimentally and attempts are made to carefully
control or eliminate extraneous variables (Reese and Lipsett, 1970).
A high degree of control over extraneous variables often places
limitations on the type of task.
Examples of some tasks typical of
feedback studies have been tracking tasks (Welford, 1968) and line
drawing tasks (Trowbridge and Cason, 1932).
In tracking tasks, a track
is drawn on a strip of paper that passes vertically downward past a
window.
The track moves irregularly troo side to side of the paper
and the subject attempts to follow it by novlng a pen from side to
side with a steering wheel,
lie observes any dissonance between the
positions of track and pen and taken action to bring the two into
alignment.
In line drawing tasks, the subject is expected to draw a
line of a given length (unknown t" hlsa).
This Is acconplished by
providing him with feedback inforaatlun for sequential correction of
his responses.
While the study of feedback iu relatively isolated conditions
nay clarify its role in learnings
perturstance, one of the basic
problems Is that of gencralizatiiacural settings.
Education takes
19
place In settings in which extraneous variables go uncontrolled and
successful performance Is determined primarily by curriculum requirements.
Thus, research conducted for educational purposes should be based on
tasks which are age and curriculum related.
Control can be applied with
respect to such factors as presentation time, stimulus consistency,
and standardized administration conditions.
The purpose of this
study therefore, was to examine the component disability of choice
(monitoring) in the context in which the student learns and manifests
his disability.
Design of the Monitoring Tasks
In this study, tasks requiring the monitoring of selfgenerated and externally-generated errors were designed and adminis­
tered.
The tasks were designed to be logically consistent with the
definition of the monitoring component disability (an impairment in
the ability to detect self-generated or externally-generated errors).
Five tasks were designed to discover whether a monitoring
deficit would be a good indicator of learning disability.
of errors were studied:
generated errors.
Two types
(1) self-generated errors, and (2) externally-
Task One dealt with self-generated errors, and
Tasks Two, Three, Four, and Five dealt with externally-generated
errors.
Each cask is described below along with directions for
administration.
Task One:
Creative Writing Task
Description.
Photographs taken froea the Scholastic Achieveasnt
"Images of Man" kit (Saith et al., 1972) were ustd for the Creative
20
Writing Task.
The photographs used were entitled: "San Salvador, 1970",
"East 100th Street, 1968-1970", and "London, anti-Nazi Protest". For
this task, each student was shown a photograph and asked to write a
story about it.
for analysis.
A writing sample of approximately 100 words was necessary
If 100 words were not produced from the first photograph,
the second and third were used.
After writing the story, the student
was given a red pencil and asked to carefully read his story(ies)
and circle any mistakes he had made or any mistakes he thought he
had made.
No time limit was imposed.
Directions for Administration. "I'M GOING TO SHOW YOU A
PHOTOGRAPH.
I WOULD LIKE YOU TO WRITE A STORY ABOUT IT.
YOU CAN LOOK
AT THE PHOTOGRAPH AS OFTEN AS YOU WISH AND YOU CAN WRITE ANY TYPE
OF STORY YOU WOULD LIKE TO ABOUT IT. JUST TRY TO WRITE THE BEST
STORY YOU CAN."
After writing the story the student was given a red
pencil and was told:
"NOW I WOULD LIKE YOU TO GO OVER WHAT YOU HAVE
JUST WRITTEN AND CIRCLE ANY ERRORS YOU MAY HAVE MADE OR THINK YOU
MADE."
Task Two:
Editing Task
Description.
task.
Figure 1 shows the passage used for the editing
Each student was given a typed passage and was asked to care­
fully edit, or proof-read, the passage for any mistakes.
The typed
passage had a total of 35 errors consisting of errors in spelling,
capitalization, punctuation, and grammar.
The student was asked to
find and correct as many of the errors as possible.
time limit.
There was no
21
Example:
After the Game were over:
too a cowboy movey.
Joe and pete went
Back in 1934 Jim Taylor and his family of four spend
a good part of the year picking crops, they starrted
out early in January in the Imperial Valley. And drifted
northward, picking diferent crops as they rippened.
they got payed almust 2.50 a day). Inn July; when the
beans' and peas' begun to ripen, they went to Silver
county and stayed their until the snow fell?
Jim had hoped to make enuf money in his bean and pea
pickin in Silver County to move his family South again
so they could work the winter crops. But his fourman
paid them only halve of their earned wages and Tony, his
youngest sun, became deathy sick. These curcumstances
forced the family to stay where they were with no work
and with no money. Altho the rest of the country was
coming out of the Great depression, the Taylors' was
just bearly getting buy.
Figure 1.
Editing Task passage.
Directions for Administration.
PASSAGE THAT HAS SEVERAL ERRORS IN IT.
CORRECT AS MANY ERRORS AS YOU CAN.
"I'M GOING TO GIVE YOU A
I WOULD LIKE YOU TO FIND AND
THERE ARE SPELLING ERRORS,
CAPITALIZATION ERRORS, PUNCTUATION ERRORS, AND ERRORS IN GRAMMAR.
IF
YOU KNOW THAT SOMETHING IS WRONG BUT YOU AREN'T CERTAIN HOW TO
CORRECT IT, CIRCLE THE MISTAKE ANYWAY.
Task Three:
LET'S TRY THE EXAMPLE FIRST."
Yes-No Spelling Task
Description.
Figure 2 shows the words which were used in a
spelling task in which the student was shown a total of 50 words, one
at a tiiae.
Half of the words were correct and half were incorrect.
The words were arranged in random order by a Cable of random numbers.
22
Example A
Example B
Example C
1. style
2. thumb
3. noise
4. suger
5. piano
6. clowdy
7. gossup
8. fallicy
9. forfeit
10. boycott
11. defence
12. sceince
13. fulfil
14. priorty
15. drissle
16. control
17. disease
18. beneth
19. souvenir
20. applaudes
21. mediocre
22. obsticle
23. sentense
24. mariage
25. innocent
Figure 2.
band
think
childran
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
inferior
arguements
believing
permanent
picknicing
necessary
prejudise
allowence
oxidation
earthquake
atmosphre
exagerate
excellence
scholastic
proficiency
enviornment
discernable
cumbustible
television
grandfarther
compostion
occasionally
enthusiastic
embarrassment
conscientious
Yes-No Spelling Task
Each word was typed on a three by five card.
one and one-half seconds.
said the word.
The word was exposed for
Just before exposing the word, the examiner
The student was asked to circle a "+" (representing
a "yes") on an answer sheet if the word shown to him was spelled
correctly; if the word was spelled incorrectly he was to circle a
(representing a "no").
23
Directions for Administration. "I'M GOING TO SHOW YOU WORDS,
ONE AT A TIME.
THEY WILL BE SHOWN TO YOU FOR ONLY ABOUT TWO SECONDS.
HALF OF THE WORDS WILL BE SPELLED CORRECTLY AND HALF OF THE WORDS WILL
BE SPELLED INCORRECTLY.
AFTER YOU HAVE SEEN THE WORD, CIRCLE A PLUS
("+") IF THE WORD IS CORRECT, AND A MINUS
INCORRECT.
IF THE WORD IS
I WILL ONLY SHOW THE WORDS TO YOU ONCE.
LET'S TRY THE
EXAMPLES FIRST."
Task Four:
Two-Alternative Forced-Choice Spelling Task
Description.
Figure 3 shows the words used in a spelling task
which involved presenting a student two spellings of the same word
(one correct and one incorrect) in a single exposure.
words was used.
A total of 50
Each pair of words was typed on a three by five card.
The card was exposed for two and one-half seconds.
posing each card, the examiner said the word.
Just before ex­
If the first word was
spelled incorrectly, the student was to circle a "1" on his answer
sheet; if the second one was the incorrect spelling he was to circle
a "2".
Directions for Administration.
"I'M
GOING
TO SHOW YOU SOKE
MORE WORDS; THIS TIME I WILL SHOW YOU TWO AT A TLME.
SHOWN TO YOU FOR ONLY ABOUT THREE SECONDS.
THEY WILL BE
ONE OF THE WORDS IS
SPELLED CORRECTLY AND ONE OF THE WORDS IS SPELLED INCORRECTLY.
Al'tER
YOU HAVE SEEK THE WORDS CIRCLE A "1" IF THE FIRST WORD IS THE GKE
SPELLED INCORRECTLY; CIRCLE A "2" IP THE SECOND WORD IS IKE IJiCUKRECT
SPELLINC.
LET'S TRY THE EXAMPLES FIRST."
24
Example A.
Example B.
Example C.
1)
2)
3)
4)
5)
6)
7)
8)
9)
10)
11)
12)
13)
14)
15)
16)
17)
18)
19)
20)
21)
22)
23)
24)
25)
1
forty
truely
nickle
sltrus
milage
acrobat
absence
pluramer
reciept
plateau
bicycle
holliday
succeed
corduroy
alphabet
intrance
dandelion
morgage
calender
pamflet
business
nuscence
dilagence
consoling
conscious
Figure 3.
Task Five:
2
fourty
truly
nickel
citrus
mileage
acrabat
absnece
plumber
receipt
platow
bycicle
holiday
succede
cordoroy
alphebet
entrance
dandilion
mortgage
calendar
pamphlet
bissness
nuisance
diligence
consouling
consious
1
milk
shcool
president
26)
27)
28)
29)
30)
31)
32)
33)
34)
35)
36)
37)
38)
39)
40)
41)
42)
43)
44)
45)
46)
47)
48)
49)
50)
2
melk
school
presadent
1
sincerly
ascertain
curriculum
abdminal
occurance
procedure
melanchaly
neumonia
vegetable
committee
sindicate
secretary
defensible
restaurant
vallentine
commitment
inditement
experiance
inaugurate
maintenance
enforcable
amphetamine
temperarily
congratulate
enstallation
2
sincerely
assertain
cirriculum
abdominal
occurrence
prosedure
melancholy
pneumonia
vegtable
committe
syndicate
secratary
defensable
resturant
valentine
committment
indictment
experience
inaugerate
malntainance
enforceable
amphatemine
temporarily
congradulate
installat ion
Two-Alternative Forced-Choice Spelling Task
Vocabulary Task
Description.
Figure 4 shows the Vocabulary Task.
This task
involved presenting students with fifty pairs of words, half of which
were synonyms and half of which were not synonyus.
was typed on a card (10 pairs per card).
read to the student.
Each pair of words
The pairs were shown and
There was no tia« ltait for exposure or response.
25
Examples:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
tidy
neat
pantile--—suspire
abandon
desert
colossal
gigantic
diminish
create
expand
lend
arrogance
Ignorance
baffled
confused
bleak
desolate
hexagon
nuisance
chastisement
punishment
pomp
hope
former
costly
timid
shy
succeed
achieve
quaint
nearsighted
opt inistic
hopeful
elucidate
explain
subtle
inferior
unworthy
cruel
dissimilar
unlike
transparent
opaque
ignorant
stupid
menace
threat
convicted
refused
complex
horizontal
migrate
move
Figure 4.
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
45.
46.
47.
48.
49.
50.
relevant
comfortable
solemn
grave
stupor
fortune
d iff icult
hard
decrease
copy
oppose
control
apprehensive
fearful
evident
obvious
reject
unite
resident
occupant
appraise
estimate
vertical
dangerous
erosion
protection
f ic ti tious
imaginary
inc rement
increase
flexible
sharp
maimed
rescued
obsolete
old
perennial
perpetual
loiter
complain
protrude
ache
refuted
disproved
scrutinize
examine
expand
profit
maximum
tight
Vocabulary Task
Students were asked to respond to each pair of words on a scale of
one to five:
"1"—absolutely certain that words were synonyms;
"2"--Partially certain that words were syaonyms; "3"—uncertain whether
the words w«rc synunyaa or not synonyms; "4"--partially certain the
words were
iwt
syuonysaa;
synouywL*.
For
the
bydunyiu
wcic
"^''--absolutely certain the words were not
purpose
of
this task, pairs of words that were not
considered to be errors.
Directions for Administration.
PAIRS OF WORDS.
"I'M GOING TO SHOW YOU SOME
HALF OF THE PAIRS ARE SYNONYMS (THAT IS, WORDS THAT
MEAN ABOUT THE SAME THING) AND HALF OF THEM ARE NOT SYNONYMS (THAT IS,
THEY ARE WORDS THAT DO NOT MEAN THE SAME THING).
SET OF WORDS TO YOU.
I WILL READ EACH
AFTER YOU HAVE SEEN AND HEARD EACH SET OF WORDS
I WANT YOU TO SHOW HOW CERTAIN YOU ARE THAT THE WORDS ARE SYNONYMS BY
CIRCLING A NUMBER FROM ONE TO FIVE.
IF YOU ARE ABSOLUTELY CERTAIN
THAT THE WORDS ARE SYNONYMS, CIRCLE "1"; IF YOU ARE PARTIALLY CERTAIN
THAT THE WORDS ARE SYNONYMS CIRCLE "2"; IF YOU ARE UNCERTAIN WHETHER
THE WORDS ARE SYNONYMS OR NOT, CIRCLE A "3"; IF YOU ARE PARTIALLY
CERTAIN THAT THE WORDS ARE NOT SYNONYMS, CIRCLE A "4"; AND IF YOU ARE
ABSOLUTELY CERTAIN THAT THE WORDS ARE NOT SYNONYMS, CIRCLE A "5". LET'S
TRY THE EXAMPLES FIRST."
Conditions of Task Administration
Task One (Creative Writing Task) was administered first to all
students.
The regaining tasks (Two through Five) were put in random
order for each student by assigning a number to each test and using a
table of random numbers.
The tasks were individually administered to
all subjects by the investigator in a private room In the school that
the student attended.
The administration time per student was
approximately 55 minutes.
Signal Detection Theory
A model of human performance which appears to be appropriate
to the study of ewnitorlng deficits is signal detection theory.
Extensive explanations of signal detection theory may be found in
27
Swets, Tanner, and Birdsall (1961), Swets (1964), and Sheridan and
Ferrell (In press).
Signal detection theory has mainly been applied
in psychophysics; in this study it will be applied in psychoeducation
by modeling error detection as a signal detection process.
In the fundamental detection problem, an observation is made
of events occurring in an interval of time, and a decision is made,
based on the observation, whether the interval contained only the
background interference or a signal as well.
The background interference
is assumed to be random and is referred to as noise (N); the other
alternative is signal plus noise (SN).
Noise is always present,
whereas the signal may or may not be present during the specified
observation interval.
The noise may be either external due to vari­
ability of the stimulation presented to the subject or interval due
to randomness in the activity of the central nervous system (Welford,
1968, p. 32).
The decision made depends upon two factors: (1) the sensitivity
of the subject to the signal strength (d'), and (2) whether or not the
observation exceeds a criterion adopted by the subject in a given
situation.
It is the analysis of both of these factors that differ­
entiates signal detection theory from traditional threshold theories.
Threshold theories do not take account of criterion values.
Sensitivity
to signal (d1) is an index of detectibility which increases as the
differences between noise (N) and signal plus noise (SN) increases.
The decision a subject renders in attempting to detect signals will
have one of four possible outcomes:
the observer nay say "yes" or "no"
28
and may in each case be correct or incorrect.
In other words, the
decision outcome may be a hit, (sn|SN), saying signal when signal is
present; a miss, (n|SN), saying noise when signal is present; a
correct rejection (n|N), saying noise when noise is present; or a
false alarm. (sn|N), saying signal when only noise is present.
These four outcomes are interdependent in that an increase in
the probability of a hit, (sn|SN), can be achieved only by accepting
an increase in the probability of a false alarm, (sn|N) and decreases
in the other probabilities.
In order to detect the presence of SN or N
in a given interval, the subject is thought to establish a subjective
criterion by which he decides whether or not to acknowledge the
presence of a signal.
This decision criterion has been shown to be
generally Independent of the sensitivity of the subject and dependent
upon such non sensory factors as attitudes and motivation.
The
criterion established by a subject may vary in conservativeness or
laxness from one setting to another.
A given criterion yields a particular balance among the prob­
abilities of the four possible outcomes; conversely, the balance
desired by an observer in any instance will determine his optimal
criterion.
Swets, Tanner, and Bird6all (1961) summarize the detection
process according to signal detection theory in the following:
The particular decision that is made depends upon whether
or not the observation exceeds a criterion value; the criterion
in turn depends upon the observers detection goal and upon the
Information he has about relevant parameters of the detection
situation. The accuracy of the decision that is made is a
function of the variable d' which is monor.onically related to
29
the signal strength. . . . The main thrust of this con­
ception . . . is that more than sensory information is in­
volved in detection. Conveniently, a large share of the
non-sensory factors are integrated into a single variable,
the criterion (p. 51).
When monitoring, the student is presumed to have to decide
whether a particular item is in error or not.
He makes that decision
as if he were to (1) observe the item and relate it to what he knows;
(2) generate an internal scalar variable monotonic with the probability
that the item is in error given both the observation and what he
knows; and (3) decide it is in error if the internal variable is
larger than or equal to a specific criterion level, or decide it is
not in error if it is less than that criterion.
The criterion is
presumed to be sensitive to the cost, rewards, and likelihood of
errors.
Observations may be represented as varying continuously along
a single dimension and any one observation may arise either from
noise alone or signal plus noise.
Figure 5 portrays two hypothetical
distributions along a single dimension.
The observation, labeled x,
is plotted on uhe abscissa.
The left hand distribution is the one
resulting from noise alone.
The right hand distribution represents
signal plus noise.
Since the observations will tend to be of greater
magnitude when a signal is presented the mean of the SN distribution
will be greater than the mean of the N distribution.
In general, the
greater the intensity of the signal the greater the separation of
means.
30
•H >,
HU
•H -H
Observation (x)
Figure 5.
Hypothetical noise and signal plus noise
distributions.
The process of signal detection is therefore viewed as being
a choice between two normally distributed variables.
One, having a
mean equal to zero, is associated with noise alone; the other,
associated with signal plus noise has a mean of d'.
In the typical
detection problem, the subject decides from which dlecrlbution the
observation came.
Data Collection
Two sources of data were Involved In this study:
(1) judges'
estimates and test data In combination tor the selection of the two
saaple groups, and (2) performance of the two saaple groups on the
monitoring tasks.
The sampling procedure Is described in Chapter III,
and the results of saaple performance on the aanicoring casks is jjiven
in Chapcer IV.
CHAPTER III
SAMPLING PROCEDURE
Replication of research studies 1s facilitated if the ex­
perimental samples are carefully defined.
This chapter will outline
the procedure for delineating the learning disability population
used in this study.
The population was systematically refined tl.rough
the following steps:
(1) selection of the initial population,
(2) selection through specialist ratings, and (3) confirmation
through test data.
Results of each step will be given under the
appropriate section.
Initial Population
For the initial sample, teachers were asked to submit the
names of students between the ages of 14 and 17:
(1) who were having
difficulty in school in successfully meeting established academic
standards, and (2) who were not evidencing any learning difficulties
and were achieving at an average rate.
Twency-uevtn tcachcra from
three Tucson high schools (representing a total student enrollment
of 5,100) participated in this selection step.
The n sumta o f 2 6 0
students with learning difficulties and tins naocs ut 110 atudents
without learning difficulties were submitted.
31
32
Specialist Ratines
The cumulative folder for each of the submitted names was
reviewed and the following information was extracted:
age, sex,
grade, achievement test scores, psychological test scores, remedial
procedures and results, clinical impressions, and other pertinent
information such as medical background.
Data on each student were
placed on a summary sheet to be submitted to specialists in learning
disability.
The forms for this procedure were developed in a previous
study by DeRuiter (1973).
Appendix B shows a sample summary sheet
and instructions for specialist ratings.
Specialists were defined
as individuals who had at least two years of graduate training in
learning disability and at least three years of experience in the
diagnosis of learning disability.
Procedure
A total of 12 clinical specialists were aslced to rate the
probability that each of the 370 students in the initial sample had
a learning disability.
(specialists.
Each student was independently rated by three
The specialists were asked to rate each child on a
scale of one to 100.
For purposes of explanation, the Instructions
froea the DcJtulier ior» (1973) are given below:
33
INSTRUCTIONS
Based on the data in the data sheet, please rate each child
on a percentage scale below according to your estimate of the
probability that the student has a learning disability, using
your own definition. A rating above 50% indicates that you
think the student is learning disabled. A rating of exactly
50% indicates that you are uncertain or do not have sufficient
data to make a judgment. Please fill in the case number.
EXAMPLE;
Case number
student definitely
is not LD
0
uncertain whether
student is or is not LD
25
50
student definitely
is LD
75
100
INTERPRETATION OF EXAMPLE:
The star (*) shows that the student is rated at approxi­
mately 72%. Therefore, the rater thinks he is learning
disabled, and the rater is 72% certain that this decision
is correct. That is, the rater thinks that 72% of the
students who have data of the type given on this student
would be judged by him to be learning disabled.
A student was selected for the learning disability group if
the following criteria were met:
(1) each of the three specialists
rated the student's probability of having learning disability as at
least 55%, and (2) the average of the three specialists' probability
rating was at least 60%.
A student was selected for the non-learning
disability group on the basis of two criteria: (1) each of the
three specialists rated the student's probability of having learning
disability as no more than 45%, and (2) the average of the three
specialists' probability ratings was no greater than 40%.
Results
This phase of sample refinement resulted in the selection of
36 students for the learning disability group and 36 for the nonlearning disability group.
The resulting two groups of students are
described in Tables 1 and 2 in terms of age, grade, individual
specialist estimates, and average specialist estimates.
Table 1
describes the learning disability group and Table 2 the non-learning
disability group.
The cases in each table are arranged according to
chronological age.
Twenty-three females and 49 males made up the sample of 72
students.
The average age for the learning disability and the non-
learning groups was 15-7 and 15-4 respectively.
The subjects in the
learning disability group ranged in age from 14-0 to 17-2.
The age
range for the non-learning disability sample was 14-0 to 17-1.
The
grade levels for all subjects ranged from ninth through 11th grade.
The Roman numerals in the tables represent the first, second, and
third ratings for that student, and not a specific clinician.
Individual ratings ranged from .55 to .95 for the learning disability
group and from .01 to .35 for the non-learning disability group.
The three probabilities were averaged for each student.
These averages ranged from .60 to .92 for the learning disability
group and from .02 to .23 for the non-learning disability group.
An
average for each group was also obtained by summing all of the
individual probability estimates for the group and dividing by the
total number of estimates.
The average group probability estimates
35
Table 1.
LD group sample selection data.
Case Number
Age
Grade
I
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
14-0
14-1
14-2
14-3
14-4
14-4
14-5
14-5
14-6
14-6
14-10
15-0
15-0
15-1
15-2
15-6
15-7
15-9
15-10
15-10
16-0
16-1
16-1
16-2
16-2
16-3
16-3
16-4
16-5
16-7
16-8
16-9
16-9
17-1
17-0
17-2
9
9
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
.55
.80
.60
.60
.75
.90
.55
.62
.55
.75
.90
.60
.55
.55
.90
.60
.70
.70
.55
.55
.60
.60
.90
.75
.90
.60
.65
.55
.90
.80
.65
.90
.90
.70
.90
.80
Specialists Estimates
II
III
Ave.
.80
.90
.60
.55
.67
.85
.62
.70
.80
.70
.80
.62
.75
.70
.80
.80
.60
.65
.80
.80
.85
.60
.85
.75
.90
.65
.75
.60
.85
.60
.90
.62
.62
.55
.90
.55
.70
.85
.60
.75
.55
.80
.70
.80
.70
.65
.85
.70
.70
.80
.75
.65
.60
.65
.70
.60
.80
.65
.80
.70
.95
.70
.55
.75
.80
.70
.80
.75
.85
.75
.90
.60
.68
.85
.60
.63
.66
.85
.62
.71
.68
.70
.85
.64
.67
.68
.82
.68
.63
.67
.68
.65
.75
.62
.85
.73
.92
.65
.65
.63
.85
.70
.78
.76
.79
.67
.90
.65
36
Table 2.
NLD group sample selection data.
Case Number
Age
Grade
I
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
14-0
14-0
14-2
14-3
14-5
14-6
14-6
14-7
14-8
14-9
15-0
15-0
15-0
15-1
15-1
15-1
15-3
15-3
15-4
15-4
15-4
15-4
15-5
15-7
15-9
15-9
15-10
15-10
15-10
15-11
15-11
16-1
16-2
16-6
16-11
17-1
9
9
9
9
9
9
9
9
9
9
9
9
9
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
11
11
11
.01
.10
.33
.20
.15
.15
.15
.20
.10
.25
.25
.25
.05
.01
.05
.05
.25
.20
.20
.10
.10
.05
.05
.15
.05
.04
.10
.10
.10
.10
.05
.02
.06
.15
.10
.15
Specialists' Estimates
II
III
Ave.
.05
.01
.20
.25
.05
.10
.05
.20
.15
.10
.15
.10
.05
.01
.01
.05
.10
.10
.15
.15
.05
.05
.04
.10
.05
.05
.05
.15
.01
.05
.10
.05
.10
.10
.35
.15
.02
.01
.15
.10
.15
.10
.10
.15
.05
.20
.01
.10
.05
.05
.10
.05
.05
.03
.10
.35
.01
.05
.25
.03
.01
.25
.05
.05
.01
.01
.01
.05
.05
.20
.15
.20
.03
.04
.23
.18
.12
.12
.10
.18
.10
.18
.14
.15
.05
.02
.05
.05
.13
.11
.15
.20
.05
.05
.11
.09
.04
.11
.07
.10
.04
.05
.05
.04
.07
.15
.20
.17
37
were .72 for the learning disability group and .10 for the nonlearning disability group.
Test Data
The Wissink (1972) and DeRuiter (1973) studies suggested that
Bayesian statistics are useful when applied to subjective probability
estimates of specialists and to test data for identification of
learning disability.
DeRuiter used the Bayesian approach on psycho­
metric data with elementary school children (ages seven through 12).
This study replicated the same procedures, but used a different age
group (ages 14 through 17).
The procedures for gathering test data were (1) selection of
appropriate tests, (2) administration of tests to the samples that
were selected according to specialist ratings (described in previous
section), and (3) analyzing results of testing.
Test Selection
In this study, an attempt was made to select the smallest
number of tests which in combination would confirm the presence or
absence of the condition of learning disability as indicated by the
specialists' ratings.
were selected.
Four tests (producing a total of eight scores)
The choice of four is based on the findings of
DeRuiter (1973) where Bayes applied to five out of 17 scores effectively
identified learning disability.
The tests were chosen primarily on the basis of the Wissink
(1972) and DeRuiter (1973) findings regarding component disabilities
38
with high diagnosticity values. In addition, tests were selected
which represent high school age-related curriculum requirements.
The selected tests are described below:
1.
Reading Comprehension test from the Peabody Individual
Achievement Test (Dunn and Markwardt, 1970).
This test is
designed to measure the ability to derive meaning from the
printed word and the context.
Subjects are required to read
a passage silently and then select one of four pictures which
most accurately represents the meaning conveyed in the passage.
The score is the number of correct answers, which is trans­
formed into a standard score, age-equivalent score, or a
percentile rank.
Test-retest reliability coefficients are
reported as being .61 for grade 8 and .63 for grade 12.
The median reliability coefficient (grades K-12) is .64.
This test was standardized on approximately 3,000 students
throughout the United States.
Reading comprehension is con­
sidered to be an important factor in learning at the high
school level because of obvious curricular requirements.
2.
Mathematics test from the Peabody Individual Achievement
Test (Dunn and Markwardt, 1970).
This test is designed to
measure the ability of students to apply mathematical con­
cepts to the solution of problems.
The subject is required to
select the best of four answers to arithmetic problems of
increasing difficulty.
Writing instruments are not used.
The score is the number of correct answers which is trans­
formed into a standard score, age-equivalent score, or a
39
percentile rank. Test-retest reliability coefficients are
reported as being .76 for grade 8 and .84 for grade 12. The
median reliability coefficient (grades K-12) is .74.
This
test was standardized on approximately 3,000 students through­
out the United States.
Mathematics and the ability to apply
basic mathematical concepts to the solution of problems is
considered to be an important factor at the high school age
level because of curricular requirements.
3.
Blending test from the Stanford Diagnostic Reading Test,
Level II (Karlsen, Madden, and Gardner, 1966).
This test is
designed to measure the student's ability to synthesize the
parts of words from a visual stimulus into a whole word.
The score is the number of correct answers which can be
transformed into a percentile score.
The split-half (odd-even)
reliability coefficient is reported to be .94. This test was
standardized on approximately 12,000 cases.
Blending is
considered to be an important factor at the high school age
level because of speed being an important performance variable.
The ability to quickly synthesize parts into wholes aids
comprehension of content material.
The entire Stanford Diagnostic Reading Test, Level II was
normed on students between middle grade four to the middle
of grade eight.
While the subjects in this study were above
grade level, the blending subtest was used for three reasons:
(1) the authors state that this test evaluates the most
difficult word recognition skill tested in the battery;
AO
(2) other tests which met definitional, reliability, and time
criteria were not available; and (3) interpretation of the
scores for the purpose of differentiating learning disability
from non-learning disability was not dependent upon using
normed information.
4.
Picture Story Language Test (Myklebust, 1965).
This test was
designed to provide a means of "quantifying one's facility
with the written word and thereby provide a measurement of
this type of verbal behavior in a given individual" (Myklebust,
1965, p. 70).
This test is administered by placing a stimulus
picture of a boy playing with toys in front of the subject,
who is requested to write a story about the picture.
Five
scores result from the test, three of which are measured on
a productivity scale and one each on syntax and abstractconcrete scales.
These five scores were treated as separate
variables in the analysis of the data in this study.
Odd-
even reliability coefficients for two of the five scores
yielded by this test ranged from .38 to .92 (Myklebust, 1965,
p. 150).
years.
The coefficients were highest for ages below 11
This test was used in an extensive study of learning
disability and non-learning disability and, when used in a
discriminant analysis procedure, each of the scores was an
effective discriminator between these groups (Myklebust and
Boshes, 1969).
A test of written expression is considered to
be an important factor in learning and performance at the
41
high school level because of the heavy curricular demands
placed on students to fulfill written assignments.
Test Administration
The four tests were individually administered to all subjects
in a private room which was set aside for testing in the school that
the student attended. All testing was completed by the investigator.
The testing time for each child varied from 50 minutes to one hour.
The four tests were administered in random order.
This was accomplished
by assigning a number to each test and using a table of random numbers.
The raw scores are presented in Appendix C.
Results
In this study, the Bayesian technique was used to determine
the likelihood that learning disability was present given particular
test scores.
A number of statistical steps were followed:
(1) estimation of prior probabilities, (2) estimation of beta
distributions, (3) calculation of likelihood ratios, and (4) calculation
of posterior probabilities.
Prior Probabilities.
Each of these steps is explained below:
Prior probabilities represent the state
of knowledge prior to observations of a specific event or condition.
They refer to the probability that any one of a number of possible
mutually exclusive and exhaustive hypotheses is true.
For this study, two hypotheses were used:
that learning disability is present,
non-learning disability is present,
(1) the hypothesis
and (2) the hypothesis that
*n
t ^ 8 8 t u < *y»
exactly
42
one-half of the students in the total sample were learning disability
and one-half were non-learning disability.
Therefore, the prior
probability used for the calculation of posterior probabilities in
this study was .5 for each group.
Beta Distributions.
When a variable is limited in range, the
beta distribution provides a useful model for its distribution.
In
this study, the test scores were limited in range because of the
limited sample size.
sample group.
Beta distributions were obtained for each
The likelihood that any score indicates the presence
of learning disability is ascertained (1) by determining the height
of the beta curves at a particular score on a test, and (2) by
determing the ratio between the height of the learning disability
curve and the non-learning disability curve at that score.
The
primary use of the beta curves is to calculate likelihood ratios,
not to interpret the curves themselves.
In order to estimate the beta distributions of the test scores
in each group, each of the eight sets of students' scores was rescaled
into the range zero to one.
The procedure for this was to (1) subtract
the minimum possible score on the test from the score obtained by
the student and (2) divide the result by the difference between the
maximum possible score and the minimum possible score on the test.
These transformed scores were used to obtain the derivative distributions,
each of which was assumed to have a density of
f
1„ x
<X>< "
1
(m^» n^/
XV^I-XA"1.
(1)
43
The parameters of the beta distribution, m and n, wejre
estimated from the observed mean (X) and variance (d^) of the rescaled
distribution, as
n «
—
X(l-X)-rf2 , and
a
m ™
Xn
~— .
1-X
The resulting m and n values for the beta distributions are given in
Appendix D.
Figures 6 through 13 show the beta distributions obtained
for the learning disability and the non-learning disability groups.
Likelihood Ratios.
As noted before, beta distributions are
derived for the purpose of calculating likelihood ratios.
Likelihood
ratios were derived for each student's score by dividing the height
of the ordinate at that score in the learning disability beta
distribution by the height of the ordinate at that score in the
non-learning disability distribution.
The formula is:
f<X>LD
LR(X) -
f,Y,
.
(2)
NLD
The likelihood ratios for the two sample groups are given in
Appendix E.
A likelihood ratio of exactly one means that the ratio
between the probability of that score in the learning disability
sample and the probability of that score in the non-learning disability
sample is one to one.
A likelihood ratio of more than one indicates
learning disability, and a likelihood ratio of less than one indicates
non-learning disability.
44
5
NLD Group
4
3
f(X)
2
LD Group
1
Figure 6.
Beta distributions for reading comprehension—Peabody
Individual Achievement Test.
5
NLD Group
4
LD Group
3
f(X)
2
1
0
Figure 7.
5
10
15
20
Beta diutrlbuiions for abstract-concrete—Picture
Story Language Test.
25
45
f(X)
NLD Group
LD Group
Figure 8.
Beta distributions for blending —Stanford Diagnostic
Reading Test.
5-.
LD Group
NLD Group
3"
f(X)
2 "
1 --
19
Figure 9.
32
45
71
Beta tllscr ibut ions for Hathenaclcs—Peabudy Individual
Achievement Test.
46
5..
NLD Group
3"
f(X)
2-.
1--
0
Figure 10.
LD Group
25
75
50
Beta distributions for syntax—Picture Story Language
Test.
LD Group
f(X)
NLD Group
0
Figure 11.
100
14
28
Beta distributions for sentences—Picture Story
Language Test.
47
LD Group
f(X)
NLD Group
70
0
Figure 12.
210
140
280
350
Beta distributions for words—Picture Story Language
Test.
NLD Group
LD Group
f(X)
0
Figure 13.
17
34
Beta distributions for words/sentence—Picture Story
Language Test.
48
Posterior Probabilities.
In this study, posterior probabilities
represent probability estimates that learning disability is given a
particular set of test scores.
These were calculated by multiplying
the prior likelihood ratio (LRq) by the product of the likelihood
ratios (LR) for that set of data, and dividing the product by the
produce plus one, as in
LR " I | LR
P<»LD D1
V"1
V
(LRq II
n=l
LR>
'
(3)
+ 1
where
LR - P < V •
o
P <W
Probability of learning disability values, P(LD), were computed for
each student for all eight sets of scores.
for both groups.
Table 3 presents the P(LD)
For each group, cases are listed in order of the
probability of learning disability.
Probability estimates of less
than .001 have been listed as being equal to .001 since distinctions
between such extreme values are not very meaningful.
Examination of
Table 3 reveals that P(LD) values ranged from .99 to .03 for the
learning-disability group and from .93 to .001 for the non-learning
disability group.
Where distributions of P(LD) overlapped for the two groups, the
setting of a cut-off point was necessary in order to evaluate the
efficiency of Bayeaian procedures in separating the learning disability
and non-learning disability groups.
To maximize the number of correct
classifications the cut-off point was set at .54.
Using this criterion
49
Table 3.
Posterior probability of learning disability for each
student in the learning disability and non-learning
disability groups, given eight sets of scores.
LD Group
Case Number
P(LD)
38
40
41
42
44
45
46
48
49
50
51
54
55
56
57
58
59
60
61
62
63
65
66
67
68
69
70
71
72
52
47
43
53
37
39
64
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.97
.90
.81
.77
.75
.55
.03
NLD Group
Case Number
P(LD)
19
3
7
4
35
10
34
1
2
5
6
8
9
11
12
13
14
15
16
17
18
20
21
22
23
24
25
26
27
28
29
30
31
32
33
36
.93
.83
.30
.30
.14
.07
.02
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
.001
one student from the learning disability group (case 64) and two
students from the non-learning disability group were misclassifled
(cases 19 and 3).
A more stringent criterion was established for
selecting students for the task administration portion of the study.
The cut-off point was therefore set at .74.
With a cut-off of .74,
four students were misclassifled (cases 39 and 64 from the learning
disability group and cases 3 and 19 from the non-learning disability
group).
Thus, those included in the learning disability group had
a P(LD) > .74; those included in the non-learning disability group
had a P(LD) < .31.
No one test or set of tests accounted for these
mlsclasslflcatlons, thus suggesting that the basis for misclassificatlon
was external to the factors considered in this analysis.
Using this
cut-off point, 94% of the total sample was classified correctly.
One of the values of Bayeslan statistics is that it combines
data in a weighted fashion to determine the probability that learning
disability has been identified.
The posterior probability can be
evaluated after each piece of data has been added to Formula 3.
When
an acceptable level has been reached, additional data need not be
gathered.
The practical significance of updated estimates of P(LD)
is that one can determine whether the value of additional test
information justifies the cost of gathering that information.
For
example, if learning disability can be identified with 95Z confidence
with three pieces of test information, it is unlikely any additional
information from further testing would be justified.
51
In this study, all students were given four tests (producing)
eight measures) to determine P(LD).
To determine if all eight measures
were actually needed to identify learning disability, test data were
submitted to a Bayesian analysis in a sequential procedure.
This
sequential analysis was only performed on the group of students
Identified by the specialists as having a learning disability (Step
Two of Sampling Procedure).
Posterior probabilities were calculated
for a single test, for two tests in combination, for three tests in
combination, for four tests in combination, etc.
The percent of
learning disability youngsters identified (with a posterior probability
of .74 or greater) was determined at each step.
Tests were submitted to Bayes in the order of their diagnosticity values as computed by DeRuiter (1973) from the Wissink (1972)
data.
The sequential order in which the tests were submitted to
Bayesian analysis was the following:
1.
Reading Comprehension test from the Peabody Individual
Achievement Test (PLAT).
2.
Reading Comprehension test from the PLAT plus the AbstractConcrete score from the Picture Story Language Test (PSLT).
3.
Reading Comprehension test froa the PLAT plus the AbstractConcrete score from the PSLT plus the Blending test from the
Stanford Diagnostic Reading Test.
A.
Reading Comprehension teat froa the PLAT plus the AbstractConcrete score from the PSLT plus the blending test froa the
Stanford Diagnostic Heading Test plus the Hatheoatlcs test
from the PLAT.
5.
Reading Comprehension test from the PIAT plus the AbstractConcrete score from the PSLT plus the Blending test from the
Stanford Diagnostic Reading Test plus the Mathematics test
from the PIAT plus the Syntax score from the PSLT.
6.
Reading Comprehension test from the PIAT plus the AbstractConcrete score from the PSLT plus the Blending test from the
Stanford Diagnostic Reading Test plus the Mathematics test
from the PIAT plus the Syntax score from the PSLT plus the
Sentences score from the PSLT.
7.
Reading Comprehension test from the PIAT plus the AbstractConcrete score from the PSLT plus the Blending test from the
Stanford Diagnostic Reading Test plus the Mathematics test
from the PIAT plus the Syntax score from the PSLT plus the
Sentences score from the PSLT plus the Words score from the
PSLT.
8.
Reading Comprehension test from the PIAT plus the AbstractConcrete score from the PSLT plus the Blending test from the
Stanford Diagnostic Reading Test plus the Mathematics test
from the PIAT plus theSyntax score from the PSLT plus the
Sentences score from the PSLT plus the words score from the
PSLT plus the Words per Sentence score from the PSLT.
The first four tests represent the cocponent disabilities of
reading conprehenBlon deficit, vriting deficit, sound blending deficit,
and natheaatics comprehension deficit, respectively.
These were not
only ranked in the top ten in diagnosticity for the Wissink data (1972),
53
but the beta distributions as pictured in Figures 6, 7, 8, and 9
reveal good group separation.
The last four tests are additional
measures of the writing deficit.
Beta distributions (see Figures 10,
11, 12, and 13) indicate that these measures did not differentiate as
well between learning disability and non-learning disability.
Table 4 contains the posterior probabilities P(LD) for the
eight sets of test scores listed above for the 36 students identified
by the experts as having a learning disability.
The following observations can be made regarding the data in
Table 4.
1.
Eighty-nine percent of the cases were identified as having
learning disability after data from only three test measures
(Reading Comprehension from the PLAT, Abstract-Concrete score
from the PSLT, and Blending test from the Stanford Diagnostic
Reading Test) had been subeitted to Bayeslan analysis.
This
seems to lend credence to the notion that population identi­
fication can be accomplished economically with a minimum of
test data as Wissink (1972) and DeRulter (1973) suggest.
However, it must be added that the percent of learning
disability cases identified drops to 832 when tests four and
five are added.
This drop suggests that false positive and
false negative errors aay have been coaaitted in the identi­
fication procedure.
That is, the question of what constitutes
the best number and coabu.ation of measures must be studied
further.
This seeaa to surest tktat reliance on too little
54
Table 4. Posterior probabilities for the learning disability group
based on sequential addition of test data.
Case
Number
1 ,
2
3
.30
.99
.13
.99
.88
.96
.69
.99
.57
.91
.63
.80
.91
.63
.96
.12
.69
.51
.35
.69
.99
.99
.84
.40
.99
.99
.97
.23
.99
.57
.98
.96
.91
.94
.99
.99
.16
.99
.06
.99
.98
.99
.71
.99
.88
.99
.72
.63
.97
.28
.97
.13
.64
.95
.30
.98
.99
.99
.98
.93
.99
.99
.99
.31
.96
.96
.94
.96
.99
.99
.99
.99
.75
.99
.59
.99
.97
.99
.93
.99
.94
.99
.27
.99
.97
.75
.99
.06
.75
.99
.93
.99
.99
.99
.97
.99
.99
.99
.99
.28
.99
.99
.99
.99
.99
.99
.99
.99
Percent
Identified
61%
72%
89%
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
Conditions
5
4
6
7
8
.60
.99
.76
.99
.98
.99
.84
.99
.98
.99
.35
.99
.99
.94
.99
.33
.89
.99
.99
.99
.99
.99
.95
.99
.99
.99
.99
.21
.99
.99
.99
.99
.99
.99
.99
.99
.43
.99
.55
.99
.96
.99
.66
.99
.96
.99
.38
.99
.99
.96
.99
.15
.96
.99
.98
.99
.99
.99
.99
.99
.99
.99
.99
.33
.99
.99
.99
.99
.99
.99
.99
.99
.72
.99
.69
.99
.99
.99
.65
.99
.98
.99
.68
.99
.99
.99
.99
.72
.93
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.13
.99
.99
.99
.99
.99
.99
.99
.99
.80
.99
.30
.99
.99
.99
.81
.99
.99
.99
.91
.99
.99
.99
.99
.92
.84
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.05
.99
.99
.99
.99
.99
.99
.99
.99
.75
.99
.55
.99
.99
.99
.81
.99
.99
.99
.90
.99
.99
.99
.99
.97
.77
.99
.99
.99
.99
.99
.99
.99
.99
.99
.99
.03
.99
.99
.99
.99
.99
.99
.99
.99
89%
83%
83%
94%
94%
55
data may be misleading and may possibly be inflated by false
positive errors.
On the other hand, a decrease in the total
number of cases identified may reflect false negative errors.
The drop from 89% to 83% is attributed to the performance
of two cases (numbers 39 and A3) whose performance on the
Syntax score from the PSLT precipitously lowered their P(LD)
below the .74 cut-off point.
This may be due to the fact
that a student can get a high score on this index by writing
very few words in his story and thus decrease his chance of
making syntax errors, which is the basis for scoring this
measure.
2.
The reading comprehension measure identified 61% of the cases,
suggesting that reading deficit as a primary criterion for
learning disability is not sufficient.
3.
With the exception of five cases (37, 39, 43, 53, and 64) the
P(LD) shows a general increase as successive tests are added.
This consistent performance suggests that the group is
relatively homogeneous in nature, contrary to the popular
notion that learning disability is a heterogeneous condition.
Research Population
The sample groups used in this study were systematically re­
fined through the following steps: (1) selection of the initial
population, (2) selection through specialist ratings, and (3) confirmation
through test data .
The number of cases, ages, and grades of the
56
final learning disability and non-learning disability groups are
provided in Table 5.
Table 5.
Learning disability and non-learning disability samples as
defined by number, age, age range, and grade range.
Learning Disability
Number of Cases
Mean Age
Non-Learning Disability
34
34
15-7
15-4
Age Range
14-0 to 17-2
14-0 to 17-1
Grade Range
9 through 12
9 through 12
CHAPTER IV
RESULTS
This study attempted to differentiate between learning dis­
ability and non-learning disability in the adolescent by investigating
some characteristics which relate specifically to learning disability
at the high school level.
Identification of learning disability at
the high school level was tested through a Bayesian approach
to
psychometric test data and through a comparison of the performance of
learning disability and non-learning disability students on selected
high school tasks.
The results of the performance of both groups on
these selected tasks are presented in this chapter.
The tasks were
administered to 34 learning disability students and 34 non-learning
disability students.
The primary methodological tool used for the analysis of
results was signal detection theory.
However, signal detection theory
was not an appropriate means of analysis for two of the tasks (Task
One:
Creative Writing and Task Two:
Editing) because consistent
units of observations could not be defined.
procedures were used to analyze these tasks.
Traditional statistical
To study the differences
between the learning disability and the non-leaming disability groups
on Tasks One and Two, teats of variance and mean differences were
applied.
The F test was applied to determine if the variances of the
learning disability and non-learniug disability samples were different.
57
58
The fc-test was applied in order to note differences in central
tendency.
The results are presented by task.
Task One: Creative Writing
For this task, the student was shown a photograph and asked to
write a story.
After writing the story he was asked to proofread his
story for any errors that he had made.
Scoring Procedure
Scoring was based on a 100-word sample.
for self-generated errors.
The passage was scored
Separate scores were calculated for the
total number of errors committed, total number of errors detected, the
percent of errors detected, and total number of nonerrors detected
(that is, items indicated as being in error when in fact they were
correct).
Questionable responses were checked against the standards
for written expression in Tainter and Monro (1969).
Raw data for all
subjects are given in Appendix F.
Results
Results of F and ^-tests are presented in Table 6.
These
results indicate significant differences between the variances on
each measure and the means on each oeasure.
These results are shown
graphically in the bar diagrans in Figures 14, 15, and 16.
Figure 14
shows errors and errors detected by the non-learning disability group;
Figure 15 shows errors and errors detected by the learning disability
group; and, Figure 16 depicts the nuaber of nonerrors depicted by
each group.
Table 6.
Comparison of variances and means of learning disability and non-learning disability
groups for Task One, Creative Writing.
LD
X
SD
F
P
t
14.43
4.18
2.63
30.01
.001***
-9.25
.001***
9.59
6.87
2.71
1.66
17.11
.001***
-5.68
.001***
322
.19
64%
.29
2.40
.014**
5.41
.001***
1.71
2.10
.59
.71
8.85
.001***
Measure
X
Errors
27.44
Errors Dectected
Percent Errors
Detected
Nonerrors
Detected
*
**
***
<
<
<
.05
.01
.001
NLD
SD
-3.02
P
.004**
• Number of Errors
• Errors Detected
Overlap of errors and errors
detected
Students
12
10
6
4
2-1
]
10
Figure 14.
Q.
Errors
15
20
25
30
Errors and errors detected by the non-learning disability group
in the Creative Writing Task.
o
• Number of errors
• Errors detected
(3 Overlap of errors and errors
detected
Students
84
25
Figure 15.
xcmQ.
30
35
H
40
45
50
55
60
Errors and errors detected by the learning disability group in
the Creative Writing Task.
Errors
•Learning Disability
Non-Learning Disability
Learning Disability and
Non-Learning Disability
Students
01
Figure 16.
Qa
Nonerrors
Detected
10
TT
Number of nonerrors detected by learning
disability and non-learning disability
students in the Creative Writing Task.
63
As might be expected, the learning disability group committed
more errors than the non-learning disability group on a 100-word
sample (27.44 for learning disability and 4.18 for non-learning
disability).
The range of errors was four through 59 for the learning
disability group and zero through 12 for the non-learning disability
group.
The fact that the learning disability sample made about six
times as many errors as the non-learning disability sample may be
explained by one or a combination of the following: (1) the learning
disability group may not have learned the correct words or punctuation,
and thus had not internalized the correct response, (2) the learning
disability group may not have selected responses in the same manner as
normal learners who tend to choose words and types of sentences that
they can correctly express and avoid the use of those that are difficult
and, (3) the learning disability group may have, after years of repeated
failure, adopted a careless attitude toward performance.
The non-learning disability group detected proportionately
twice as many errors as the learning disability group (64% for learning
disability and 32% for non-learning disability).
The percentage of
errors detected may be somewhat affected by the total number of errors
made; that is, the detection problem is different when the number of
errors in the passage varies.
For example, if 50 errors are made by
one student and five by another, detectibility may be affected by
such factors as fatigue or attention.
For the purpose of this analysis,
however, the detection problem was assumed to be relatively equal in
all cases.
64
For both groups, the percentage of errors detected may be
adversely affected by curriculum emphasis.
It was reported by several
English teachers in the schools from which the samples were drawn that
correctness of expression was not emphasized as much as creativity of
expression.
This emphasis would probably inflate both the number of
errors committed as well as the errors detected.
The fact that the learning disability group was able to detect
approximately one-third (32%) of their errors suggests that they have
the potential for improving their overall school performance by this
much; that is, the first step in correcting an error is detecting it.
Once an error has been detected the student can be taught possible
ways to find the correct answer; for example, ask the teacher, ask a
classmate, use a dictionary, or some other source.
While the variance and mean differences between the two groups
were significant in nonerrors detected, the absolute number of nonerrors
detected in each instance was so small that it was not considered to
be a meaningful index in this task.
The small number of nonerrors
detected suggests that the individual's criteria for saying something
is incorrect is relatively stringent on a task involving monitoring
of self-generated errors.
Implications for Diagnosis.
Implications for diagnosis which
can be drawn from the results on the Creative Writing Task Include the
following:
1.
Performance on this task could be used to discriminate between
learning disability and non-learning disability.
65
2.
Many useful diagnostic lndlcles may be derived from a written
sample like the one used In this task.
These might include
length of response, content, and types of errors (such as
word order, word usage, and punctuation).
3.
The administration and scoring of such a task would be more
economical than a total achievement test battery in terms of
materials and time.
Implications for Remediation.
Implications for remediation
which can be drawn from the results on the Creative Writing Task
include the following:
1.
Adolescents should be made aware of the poor quality of their
own performance in written work.
The repercussions of such
performance in future employment situations are obvious.
2.
Students should be taught how to be selective in their choice
of words and sentences when using written expression so as
to limit the number of errors committed.
On the other hand,
they should not be so selective as to inhibit expression.
They should be taught to adjust their selectivity according
to assignment requirements.
3.
Since students in the learning disability sample demonstrated
that they had the potential for detecting their own errors (32Z),
they should be encouraged to check their work before turning
it in.
They should be given specific strategies or systems
for doing so.
These should be taught and practiced in remedial
sessions until the process of monitoring their own performance
66
becomes automatic.
Remediation of a monitoring deficit will
be difficult because many of the errors in performance are the
result of incorrectly learned habits.
Unlearning an incorrect
habit and relearning the correct one prolongs remediation.
Task Two:
Editing
For this task the student was given a typed passage and asked
to carefully edit, or proof-read, the passage for any mistakes.
Scoring Procedures
Performance on this task was scored according to the following
indices:
number of errors detected, number of errors correctly
corrected, percentage of errors correctly corrected, and number of
nonerrors detected (that is, items indicated as being in error when in
fact they were correct).
Raw data for all subjects are given in
Appendix F.
Results
Results of F and ^-tests are presented in Table 7. These
results indicate significant differences between the means on each of
the measures and the variances on all measures except errors corrected.
These results are shown graphically in the bar diagrams in Figures 17,
18, and 19 for three measures:
errors detected, nonerrors detected,
and errors corrected.
Discussion
The learning disability group detected 37X of the errors in
the editing passage whereas the non-learning disability group
Table 7.
Comparison of variances and means of learning disability and non-learning disability
groups for Task Two: Editing.
LD
NLD
X
SD
X
SD
13.06
6.41
27.00
4.23
2.34
Percent Errors
Detected
37%
.19
77Z
.12
Nonerrors Detected
5.65
3.12
3.29
Errors Corrected
9.41
5.59
25.53
Percent Errors
Corrected
71Z
Measure
Errors Detected
*
**
***
< .05
< .01
< .001
.17
941
F
t
P
.017*
10.52
.001***
2.34
.017*
10.52
.001***
2.08
2.33
.017*
-3.61
.001***
5.54
1.02
11.95
.001***
.09
3.40
6.88
.001***
P
NS
.ooi***
•
Learning Disability
Non-Learning Disability
Learning Disability and
Non-Learning Disability
Students
6_
4-
2_
"I
Errors
Detected
10
Figure 17.
Number of errors detected by learning disability and non-learning disability
students in the Editing Task.
o\
oo
• Learning Disability
Non-Learning Disability
Learning Disability and
Non-Learning Disability
Students
10 8 -
Nonerrors
Detected
5
Figure 18.
10
15
20
25
30
35
Number of nonerrors detected by learning disability and non-learning
disability students in the Editing Task.
o\
vo
• Learning Disability
Non-Learning Disability
Learning Disability and
Non-Learning Disability
Students
10.
8.
6.
42Errors
Corrected
10
Figure 19.
15
20
25
30
35
Number of errors corrected by learning disability and non-learning
disability students in the Editing Task.
VJ
O
detected 77% of the errors.
These percentages closely approximate
the performance for each group as on the Creative Writing Task (32%
and 64%), thus suggesting that the percentage of errors detected in
self-generated and externally-generated tasks is approximately the
same.
Unlike the detection problem in the Creative Writing Task where
the number of errors per passage varied according to each subject,
this task presented the same number of errors to each student.
The number of nonerrors detected in this task (5.65 for the
learning disability group and 3.29 for the non-learning disability
group) is considerably greater than the number detected in the
Creative Writing Task.
This difference may, in part, be explained by
the nature of the task.
First, there were one and one-half times as
many words in the Editing task as in the Writing task.
Secondly,
indicating nonerrors in one's own performance (Task One) may be less
likely than in the performance of others (Task Two) because the latter
task is not subject to the student's selective choice of elements and
constructions.
The difference in the performance of the two groups for percent
errors corrected (71% for learning disability group and 942 for the
non-learning disability group) suggests that the two groups may have
differing Internal representations of the model; that is, being able
to correct an error is contingent upon the subject having a correct
model in mind for reference.
The learning disability group, however,
did correct a relatively large number of externally-generated errors.
72
Implications for Diagnosis.
Implications for diagnosis which
can be drawn from the results on the Editing Task include the following:
1.
This measure (Editing Task) could be used to differentiate
learning disability from non-learning disability.
2.
Since the percentage of errors detected in the externallygenerated Editing Task was approximately the same as in the
self-generated Creative Writing Task, this task would be the
more economical diagnostic task in terms of time.
3.
Diagnosing correction of errors is revealing and should be
added to the diagnosis of error detection.
Such a measure
could be added to the Creative Writing Task.
A.
Analysis of types of errors could be added as a measure for
determining the type of errors the student is able to correct
and the type he is not able to correct.
Implications for Remediation.
Implications for remediation
which can be drawn from the results of the Editing Task include the
following:
1.
Students should be taught skills in correcting errors which
have been detected.
These skills might Include dictionary
skills, the use of context clues, or asking soncone for the
proper answer.
2.
Remediation which is based on externally-generated errors docs
not involve the motional overtones that resedlatlon batted on
self-g«?ueratcd errors does.
An exaaple of this was observed
when the investigator was working with a high school student
73
who had been referred for evaluation because of carelessness
in written assignments.
When the student was asked by the
investigator to write a short story and then to proof-read
his work and correct any errors that he found, he became quite
defensive, hurriedly went over the passage and offered rational­
izations for his poor performance.
When the student was given
a passage with externally-generated errors and asked to detect
and correct the errors, he willingly participated and admitted
that he liked the challenge of the task.
3.
Remediation which is based on the detection and correction of
externally-generated errors supports a basic principle of
remediation:
that of "teaching" and not "testing."
In teaching,
the student is guided toward the correct answer, whereas, in
testing the student's answers (correct or incorrect) are
accepted.
The danger in testing is that the student must prove
his failure time and time again.
Tasks Three and Four:
Spelling
The spelling task consisted of two subtasks:
a Yes-Not Spelling
Task and a Two-Alternative Forced-Choice (2AFC) Spelling Task.
A
signal detection model was used to analyze the Yes-No Spelling Task.
A
second task (2AFC) was designed to provide a check on the use of this
Bodel with yes-no data.
Yes-No Spelling Task
For this task words were shown tachistoscopically and students
were asked to circle a "+" (representing a "yes") if the word was
74
spelled correctly and a
Incorrectly spelled.
(representing a "no") If the word was
As previously described In Chapter II, signal
detection theory can be applied to certain error detection tasks.
In
a signal detection problem, observations are made in an interval of
time and decisions are made whether the interval contained a signal
plus noise, or Just noise.
In this task, the signals to be detected
were words spelled incorrectly.
Words spelled correctly were considered
part of the noise distribution.
The subject responded "yes" or "no".
It was assumed that sensitivity of the subjects to the spelling errors
(detectlblllty) and the willingness of the subject to acknowledge the
errors (criteria) could be inferred from the data.
It was further
assumed that the decision variable is normally distributed with equal
variances for correct and incorrect words.
Scoring Procedures.
according to two lndicies:
rate p(e|C).
Performance on this task was scored
the hit rate p(e|E), and the false alarm
The hit rate is the probability that an error will be
Identified when it is, in fact, present.
The false alarm rate is the
probability that a word will be said to have an error in it when, in
fact, it is correct.
Results.
Raw data for all subjects are given in Appendix F.
The data from this task were submitted to statistical
tests for determining whether the learning disability and the nonlearning disability groups could be differentiated in their (1) detectlblllty
of spelling errors (d*) and (2) criteria used in responding.
of these two lndicies will be presented In turn.
The results
75
1.
Detectibility (d') was computed for each student in the following
way:
a.
The student's performance was scored to determine hits and
false alarms. Assume, for example, that the number of hits
was 23 (that is, he said that 23 words had errors which, in
fact, did); and the number of false alarms was 3 (that is,
he said that three words had errors which, in fact, did
not).
b.
The hits and false alarms were converted into hit rate
and false alarm rate by dividing each score by the total
number of errors in the task (23/25 = .92 and 3/25 = .12).
c.
The d1 value for this hit rate and false alarm rate data
(.92 and .12) was determined by using tables compiled by
Elliot (1964) for computing d' values from yes-no
data.
The d1 value is 2.58 for p(e|E) = .92 and
p(e|C) » .12.
See Appendix G for all d' values.
Large
d' values represent good detectibility, poor detectibility
is represented by small d' values.
The mean d' for the non-learning disability group was 1.88
and the mean d' for the learning disability group was .15.
A d' value
of .15 suggests that the learning disability group could not tell the
difference between errors and nonerrors and their performance was not
much better than chance.
sensitivity to error.
A d* value of 1.88 represents much greater
A J>test was applied to the d' values for each
group resulting in a JL of 14.37 which was significant at the .001 level.
76
These results Indicate that the two groups can be differentiated
according to their detectibility of spelling errors.
Criteria measures were not computed for this task since the
learning disability group had a mean d' value of approximately zero.
Criteria measures are not meaningful in such cases.
The raw data
(see Appendix F) show that 14 of the learning disability sample scored
at or below chance (that is, anyone with p(e|C)^ p(e|E) is operating
equal to or less than chance).
For an analysis of criteria to be
meaningful, subjects should be responding in the area above the chance
line.
A meaningful measure, however, is the proportion or frequency
of "error" responses, p(e).
This measure is an index of the stance
taken by an individual or group toward saying that an error is present
in a word.
Implications about an individual's or a group's conservative-
ness or laxness about saying that errors are present can be inferred
from measures of p(e).
p(e) was calculated for each student by using the following
formula:
p(e) - p(e|E)p(e)T + p(e|C)p(c)T.
(4)
where proportion of errors, p(e) is equal to hit rate p(e|E) times the
proportion of errors in the total task p(e)^, plus the false alarm rate
p(e|c) times the proportion of correct items in the total task p(c)T«
In this Task, p(e)T and p(c)T were each .5 because half of the
words were spelled incorrectly and half were spelled correctly.
values for all students are given in Appendix H.
p(e)
77
For illustration, using the hypothetical case cited in the
section on detectibility where the hit rate was .92 and the false
alarm rate was .12, p(e) would be calculated in the following fashion:
p(e) » p(e|E)p(e)T + p(e| c )p(c)T
- (.92) (.5) + (.12) (.5)
- .46
+ .06
= .52
A p(e) of .52 means that this student responded "error" 52% of the time.
It should be emphasized that p(e) is an index of the frequency of
giving an "error" response /either p(e|E) or p(e|c)_7 and not a measure
of good or poor performance.
This can be readily seen by reversing the
hit rate and the false alarm rate scores in the above example; e.g.,
assume a p(e|E) of .12 and a p(e|C) of .92.
Substitution of these
values in Formula 4 results in exactly the same p(e) score.
Thus, one
student who performed quite well (high hit rate and low false alarm
rate) would get exactly the same p(e) score as another student who per­
formed quite poorly (low hit rate and high false alarm rate) because
they both said "error" responses with equal frequency.
The mean p(e) values for the learning disability and the nonlearning disability group were .42 and .44 respectively.
A p(e) value
less than .50 indicates an unwillingness to say "error" unless certainty
exists; a p(e) value greater than .50 indicates a willingness to say
"error" even when some uncertainty is present.
Doth groups tended to be
unwilling to acknowledge the presence of an error unless they are fairly
certain that one exists.
detection.
This is a conservative stance towards error
78
A _t-test was applied to the p(e) scores for each group, resulting
In a ^ of -1.48 and a p of .143 which was not significant. This suggests
that the likelihood of saying "error" for each group is about the same.
Discussion.
Figure 20 is presented to clarify the results that
the learning disability and non-learning disability groups can be
differentiated by detectibility but not p(e).
This figure presents
scatter-plot of the two variables /p(e|E) and p(e|C)7 for all subjects
in the Yes-No Spelling Task.
false alarm rate data.
rate, p(e|E).
It graphically presents the hit rate and
The numbers on the ordinate represent hit
False alarm rate, p(e|C), is shown on the abscissa.
A
student's performance is shown by cross-plotting p(e|E) with p(e|C).
Line C is the chance line.
If a student's performance is
better than chance, the point representing his performance will be above
that line.
For example, the performance of a student who had a hit
rate of .88 and a false alarm rate of .20 would be shown at point X.
If an individual'8 performance is equal to chance, the point representing
his performance will fall on the line.
For example, point Y, in which
the hit rate of .40 is equal to the false alarm rate of .40.
If an
individual's performance is worse than chance, the point representing
his performance will fall below the chance line.
For example, Z, in
which case the false alarm rate .40 is greater than the hit rate, .23.
The squares (•) in Figure 20 represent the performance of the students
in the learning disability group; the circles (O) represent the per­
formance of those in the non-learning disability group.
Perfect
detectibility would be represented by a point in the upper left hand
corner of this graph where p (e|K) = 1.00 and p(e|C) » 0.
Similarly, no
79
1-00r
O\
•8Q o o
©\
.6Q
••
p(e|E)
• 2Q
.80
.20
p(e|C)
Figure 20.
O© •ID -
one
tvo
one
two
Scatter-plot of p(e|E) and p(e|C) for learning
disability and non-learning disability groups
for the Yes-No Spelling Task.
non-learning disability student
or more non-learning disability students
learning disability btudent
or acre learning disability students
1.00
detectibility of errors is represented by a point in the lower right
hand corner where p(e|C)
=
1.00 and p(e|E) = 0. Therefore, scatter-
plot points representing performance that is less than perfect will be
somewhere between this upper left hand corner and the lower right
hand corner.
As can be seen in Figure 20, the majority of students in the
non-learning disability group cluster in an area closer to the upper
left hand corner of the graph indicating that their detectibility of
spelling errors is relatively good.
The learning disability group
tends to cluster around the chance line indicating that their detect­
ibility of spelling errors closely resembles chance performance.
The
mean hit rates for the non-learning disability group and the learning
disability group were .74 and .43 respectively.
This means that the
probability of the learning disability group detecting a spelling error
was less than half (.43) while that of the non-learning disability
group was considerably more than half (.74).
The mean false alarm
rates for the non-learning disability group and the learning disability
group were .13 and .39 respectively.
Thus, the probability of saying
error when no error exists was three times higher for the learning
disability group than for the non-learning disability group.
The frequency of saying "error" p(e) for both groups can also
be Been in Figure 20.
If p(e) is high (> .50), the group would tend
to cluster in the upper portion of the graph, that is, above line D.
If p(e) is low (< .50) the group would tend to cluster in the lower
portion
the graph, that is, below line D.
If p(e) is average (= .50)
the groups would cluster in the center portion of the graph, or along
81
line D.
Both groups cluster below line D indicating that both learning
disability and non-learning disability groups tended to be conservative
in giving error responses.
Two-Alternative Forced-Choice (2AFC) Spelling Task
For this task, each student was presented two spellings of the
same word (one correct and one incorrect) in a single exposure.
The
student was to select the incorrectly spelled word.
This task was presented to both groups to test the internal
consistency of the signal detection model by comparing estimates of d'
based on yes-no data with d' estimates based on 2AFC data.
It was
assumed that the decision variable was normally distributed and of
equal variance.
It was further assumed that if a subject made optimal
decisions in the Yes-No Task, the area under the relative operating
characteristic (ROC) curve in a Yes-No Spelling Task would equal the
percent of correct responses /p(elE).7 in a 2AFC Spelling Task.
An
ROC curve provides a means of plotting the relationship between two
distributions on a single curve.
In the case of yes-no data, the ROC
curve represents a cross-plot of p(e|E) and p(e|C).
ROC curves were
not actually generated for data in Che Yes-No Spelling Task but were
represented by the d' values calculated for each subject (these are
provided in Appendix G).
The percei.* of correct responses for the
2AFC task for each subject was also represented by d1 values.
Scoring Procedures.
Performance on this task was scored
according to the number of words called errors which, In fact, were
incorrect p(e|E).
Raw score data for all subjects are given in Appendix F.
82
Results,
d1 values were calculated for each subject for the
2AFC data in the following way:
1.
The percent of correct responses was determined for each
subject by dividing the number of errors correctly identified
by the total number of items in the task (50). For example,
if out of a total of 50 2AFC items a student identified 35
errors, the percent of correct responses would be 35 divided
by 50 or 70%.
2.
The d' value for this percent of correct responses was
determined by using tables compiled by Elliot (1964)
for computing values of d' for forced-choice tasks.
The d'
value is .74. Large d' values represent good detectibility
and small d1 values represent poor detectibility.
For 2AFC
problems Elliot's table lists d' values from -3.28 to +3.28,
the former representing zero percent correct responses, the
latter, 99% correct responses.
To test the internal consistency of the signal detection model
as it applied to yes-no data, a Spearman rank order correlation was
done on the d' values for all subjects from the Yes-No Task (representing
the area under an ROC curve) and the d' data from the 2AFC task
(representing the percent of correct responses).
A correlation of .85
(p • < .001) resulted, suggesting that the model can be applied to
both yes-no and 2AFC data and that similar measures of detectibility
(d1) can be derived with either type of task.
It should be noted,
however, that 2AFC tasks provide measures of d' only.
This task does
83
not give measures of criteria, as does a yes-no task because a subject
is forced into a response and thus only the frequency of correct
response is relevant.
Implications for Diagnosis. The implications for diagnosis
which can be drawn from the spelling tasks include the following:
1.
The detectibility measure of these tasks appears to be an
excellent discriminator of learning disability.
As was seen
in Figure 20, there is hardly any overlap of the two groups;
only one student from the non-learning disability group per­
formed in the range of the learning disability group.
The
aim of any identification procedure is to achieve separation
of groups on a particular measure with as little overlap as
possible.
2.
This task is economical in terms of administration and scoring.
Total time is approximately ten minutes.
Implications for Remediation.
The implications for remediation
which can be drawn from the spelling tasks include the following:
1.
The signal detection model may provide an interesting avenue
for communicating to the high school student exactly how he
is performing and what types of response strategies facilitate
or impede his overall performance.
The concepts of hit rate
and false alarm rate can be easily understood by the adolescent
and can aid both teacher and student in amending performance
strategies.
84
2.
The remediation of the deficits evidenced in this task will
be difficult.
With detectibility at about zero (and below In
several cases) students should be encouraged to check all their
work carefully and not rely upon their own judgment for
correctness or incorrectness.
They should be given clues as
to how to monitor spelling errors; for example, the fact that
making errors in certain parts of words is greater than making
errors in other parts.
3.
Remediation of monitoring deficits in this type of task may
serve to direct the student's attention to details and
facilitate his analysis of them.
Task Five:
Vocabulary
For this task, students were presented with fifty pairs of
words, half of which were synonyms and half of which were not synonyms.
Students were asked to respond to each pair of words on a scale of one
to five:
partially
"1" - absolutely certain that words were synonyms; "2" certain that words were synonyms; "3" - uncertain whether
the words were synonyms or not synonyms; "A" - partially certain
words were not synonyms; "5" - absolutely certain words were not
synonyms.
Scoring Procedure
Performance on this task was scored according to the following
rating scale:
1.
number of pairs marked "1" which were synonyms (1|S);
85
2.
number of pairs marked i« 2" which were synonyms (2|S);
3.
number of pairs marked "3" which were synonyms (3|S);
4.
number of pairs marked »4» which were synonyms (4IS);
5.
number of pairs marked IIIJH which were synonyms (5IS);
6.
number of pairs marked it^n which were not synonyms (UN);
7.
number of pairs marked •I2" which were not synonyms (2 IN);
8.
number of pairs marked ii^i' which were not synonyms (31N);
9.
number of pairs marked 'V which were not synonyms (4 IN);
10.
number of pairs marked H
which were not synonyms (5 IN).
Raw data for all subjects are given in Appendix F.
Results
Results were analyzed by determining Individual and group
relative operating characteristic (ROC) curves.
ROC curves provide a
means of plotting the relationship between two distributions on a
single curve; they represent the cross-plot of the hit rate and false
alarm rate scores.
An ROC curve can be readily generated from the
type of data available in this task; that is, rating scale data.
is done in the following taanner:
It
the hit rate score is crosu-plotted
with the false alarm rate score for each point on the rating scale.
For example, if the p(e|F) tor point "1" on the rating scale i& .40 and
the p(e|C) for point "1" is .OB, this point on the ROC is determined
by going up .40 on the ordinate and over .OS on the abscissa.
This
procedure is followed for each succeeding point on the rating ovale
(that is, "2", "3", "4", and "5") until an ROC curve can be generated
through these points.
Croup HOC curves, as bIajvti in Figure 21, were
86
1.00
NLD Group
sa
LD Group
.60-
.20.
0
.20
.60
.40
.80
p(e|C)
Figure 21.
HOC Curveu for learning disability and nonlearning diaability groups for die Vocabulary
Task.
1.00
87
formed by averaging scores for all subjects in a group at each of
the rating scale points.
The averaged score at each point on the
rating scale was used to generate the group ROC curves.
A large area under the ROC curve represents good detectibility;
a small area represents poor detectibility.
Therefore, a6 curves
approach the upper left hand corner of the graph, detectibility is
better.
The closer the ROC curve is to the chance line, detectibility
or sensitivity to error is decreased.
Figure 21 indicates that the
non-learning disability group has better detectibility than the
learning disability group for this task because it is a greater distance
from the chance line.
The mean area and standard deviation for the learning disability
group was .7588 and .09 respectively.
group .8758 and .06 respectively.
For the non-learning disability
To determine if the performance of
the two groups on this task was significantly different, a £-test was
done comparing the groups on the dependent variable (vocabulary) as
measured by the area under the ROC curves.
The resulting J: value was
5.92 which was significant at the .001 level.
Diacusolon.
The non-learning disability group was better at
detecting errors in vocabulary usage than the learning disability
group.
A significant point, however, is that the ROC curve for the
learning disability group, while below that for the non-learning
disability group, is a considerable distance above the chance line.
This can be seen in Figure 21.
88
Implication for Diagnosis.
This task appears to be a good
discriminator between learning disability and non-learning disability.
The inclusion of this task in the diagnostic process seems warranted
in that it taps a different level of functioning than those which
measure skill development, such as spelling and motor skills.
Implications for Remediation.
Implications for remediation
which can be drawn from the results on the Vocabulary Task include
the following:
1.
The Importance of a well developed vocabulary for the high
school learner cannot be overemphasized.
Success in the high
school curriculum is dependent upon a student's ability to
use content which is age-related—this process is facilitated
with good vocabulary skills.
2.
Remediation should be directed to developing a proficiency
in vocabulary which is age-related.
Remediation geared to
readiness and early school levels will not be productive and
should not be used for the secondary school learning disability
student.
Summary Discussion
The tasks for this study were chosen because they were thought
to differentiate successfully between learning disability and nonlearning disability.
Analysis of results suggest that these tasks
were effective discriminators and that the component disability of
monitoring is diagnostic at the high school level.
89
A differential comparison of the tasks can be highlighted
in the following points:
1.
An interesting contrast was noted in the performance of the
learning disability group on the Yes-No Spelling Task (Task
Three) and in their performance on Tasks One and Two.
In
the Creative Writing Task and the Editing Task, detectibility
of errors was 32% and 37% respectively; in the Yes-No Spelling
Task it was about zero.
On the other hand, false alarm rate
was relatively high (.39) in the Yes-No Spelling Task, but
minimal as measured by nonerrors detected in Tasks One and
Two.
These differences might be due, in part, to task differ­
ences; that is, the first two tasks had several types of
errors to be detected, not just spelling ones; and, students
were forced to respond to every word in the Yes-No Spelling
Task but were free to respond to any part of the Creative
Writing and Editing Tasks.
These differences in results between tasks seem to suggest
that it is dangerous to form rigid generalizations about the
performance of learning disability students in error detecting
situations.
Research is first needed on many of the task and
subject variables not controlled In this study, as for
example, previous learning, learning styles, and curriculum
exposure.
2.
While all tasks successfully differentiated between the two
groups, the Yes-No Spelling Task was the best discriminator
because there wa6 virtually no overlap of distributions.
This
90
task achieved better separation than any of the tests adminis­
tered in the selection procedure.
Standardization of this
task might be warranted for screening or diagnostic purposes.
3.
On the Vocabulary Task, the performance of the learning dis­
ability group was significantly lower than that of the nonlearning disability group.
However, their detectibility of
vocabulary errors was considerably better and in marked
contrast to their performance on the Yes-No and 2AFC Spelling
Tasks where detectibility of errors was close to zero, or the
chance line.
The difference in detectibility of the learning disability
group on these two tasks may, in part, be understood by con­
sidering the nature of each task.
The spelling task was one
demanding more automatic-type skills, whereas the vocabulary
task was more cognitive in nature.
One of the basic assumptions
underlying the condition of learning disability is normal or
near normal intelligence.
In that vocabulary is highly
correlated with intelligence, the peiformance of the learning
disability group on this task may be due to Intelligence.
The significant discrepancy between the two groups on this
task cannot be minimized, however.
The difference which does
exist, assuming normal Intelligence in each group, may also
reflect the toll taken by years of difficulty in school settings
on areas of strength (such as vocabulary) in the learning
disability population.
91
Concluding Statement
While the tasks in this study appear to be good discriminators
of learning disability, a note of caution is in order.
The identifi­
cation of the condition of learning disability is an extremely complex
problem since the presence of any factor by itself has not been
demonstrated to be either sufficient nor necessary to determine that
the condition exists.
Neither has any task or test score been found
to be the effective discriminator.
The results from these tasks should
be treated as preliminary in nature and suggestive for future research
efforts and refinements.
Also, while the component disability of
monitoring seems relevant at this age level, other component disabilities
might prove to be equally effective in differentiating between learning
disability and non-learning disability and should be studied.
CHAPTER V
SUMMARY AND IMPLICATIONS
Statement of the Problem
This study attempted to differentiate between learning dis­
ability and non-learning disability in the adolescent by investigating
some characteristics which relate specifically to learning disability
at the high school level.
Identification of learning disability at
the high school level was tested through a Bayesian approach to
psychometric test data and through a comparison of the performance
of learning disability and non-learning disability students on
selected tasks.
Monitoring Deficit
A monitoring deficit was studied as a characteristic which
would differentiate between learning disability and non-learning
disability in the adolescent.
It was defined as an Impairment in the
student's ability to detect self-generated and externally-generated
errors.
The role of monitoring, or the detection of errors in performance,
is a crucial one in both learning and performance.
To learn a skilled,
highly integrated response and to perform in an efficient manner, one
must attend and respond to feedback data generated by his own response
or external information.
92
93
Design of the Monitoring Tasks
In this study, five tasks requiring the monitoring of selfgenerated and externally-generated errors were designed and administered:
(1) Task One:
Three:
Creative Writing, (2) Task Two:
Spelling (Yes-No), (A) Task Four:
Forced-Choice) and, (5) Task Five:
Editing, (3) Task
Spelling (Two-Alternative
Vocabulary.
Two types of errors were studied: (1) self-generated errors,
and (2) externally-generated errors.
Task One dealt with self-
generated errors, and Tasks Two, Three, Four, and Five dealt with
externally-generated errors.
Data Collection
Two sources of data were involved in this study: (1) judges'
estimates and test data In combination constituted the sampling
procedure for the two groups, and (2) performance of the two sample
groups on the eonltoring tasks.
Sampling Procedure
The research population was sytsceeatieally refined through the
following steps:
(1) selection of the initial population; (2) selection
through specialist ratings; and, (3) cuutlraaiion through test data.
Initial Population
For the initial sasple, teacUcfo were asi_ed co suba.lt nanes of
student * between the ages of 14 and 1?:
in suet essf ul I
were ugi
(1)
w«re having difficulty
steeling established a^o-icsaic oUiislards, and (2) who
«rv 14en. 1 iig
au) learning dl£ t i^ult lea.
ttic aaAco of 260 students
94
with learning difficulties and the names of 110 students without
learning difficulties were submitted.
Specialist Ratings
Specialist ratings, based on available cumulative folder data,
were used to select a learning disability group and a non-learning
disability group out of the 370 referrals.
Each student's probability
of having a learning disability was independently rated by three
specialists in learning disability.
On the basis of the ratings from
12 specialists, 36 students with learning disability and 36 students
without learning disability were selected.
Test Data
Test Selection.
In this study four tests were used to confirm
the presence or absence of learning disability as indicated by the
specialists' ratings:
1.
Reading Comprehension teat, Peabody Individual Achievement
Test,
2.
Mathematics test, Peabody Individual Achievement Test,
3.
Blending test, Stanford Diagnostic Reading Test,
4.
Picture Story Language Test.
The four teats yielded eight sets of scores (Picture Story
Language Test yielded five, all other te6ts yielded one) which were
treated as separate variables In the analysis of the results.
Results.
In this scudy a Bayesian technique was used to
determine the likelihood that learning disability was present, given
95
particular test scores.
The use of Bayes' theorem required a number
of statistical steps, including: (1) estimation of prior probabilities,
(2) estimation of beta distributions, (3) calculation of likelihood
ratios, and (4) calculation of posterior probabilities.
Prior probabilities represent the state of knowledge prior to
observations of a specific event or condition.
They refer to the
probability that any one of a number of possible mutually exclusive and
exhaustive hypotheses is true.
For this study, two hypotheses were
used: (1) the hypothesis that learning disability is present, and
(2) the hypothesis that non-learning disability is present. Since
one-half of the students in the sample were learning disability and
one-half were non-learning disability students, the prior probabilities
for each group were set at .5.
Beta distributions for each of the eight sets of scores were
obtained separately for each group to provide a means of comparing
the groups.
By comparing the relative height of the beta curves at
a particular score on a test, the likelihood that the score would be
found in the learning-disability group was obtained.
The likelihood ratio for a score was obtained by dividing the
height of the ordinate from the learning-disability beta distribution
by the height of the ordinate from the non-learning-disability beta
distribution at the same level. The likelihood ratios provided an
estimate of how likely a particular scores was to be found in the
learning-disability sample in comparison with how likely it was to be
found in the non-learning-disability sample.
96
Posterior probabilities represent probability estimates that
a particular hypothesis is true, given that a particular set of
evidence is present.
Posterior probabilities were calculated from
prior probabilities and likelihood ratios by Bayes' theorem.
Posterior
probabilities were calculated for each student to determine if learning
disability was present given varied sets of test data.
The posterior
probability that a student had a learning disability ranged from .99
to .03 for the learning disability group and from .93 to .001 for the
non-learning disability group when all eight sets of test scores were
used in the analysis.
To determine if all eight test measures were actually needed
to identify learning disability, test data were submitted to a Bayesian
analysis in a sequential procedure.
This sequential analysis was only
performed on the group of students identified as being learning dis­
ability by the specialists.
Posterior probabilities were calculated
for a single test, for two tests in combination, for three tests in
combination, for four tests in combination, etc.
The percent of
learning disability youngsters identified (with a posterior probability
of .74 or greater) was determined at each step.
This analysis indicated
that fewer than eight measures were required to identify the condition
at the established cut-off level; however, the question of what
constitutes the best number and combination of measures must still be
determined.
Research Population
The characteristics of the research population were the
following: (1) 34 students in each group, (2) mean age of 15-7 for
learning disability group and 15-4 for the non-learning disability
group, (3) age range of 14-0 to 17-2 for the learning disability
group and 14-0 to 17-1 for the non-learning disability group, and
(4) grade range of 9 through 12 for each group.
Results
The primary methodological tool used for the analysis of
results was signal detection theory.
Since signal detection theory
was not an appropriate means of analysis for Tasks One and Two because
consistent units of observations could not be defined, traditional
statistical procedures were used to analyze these tasks.
Signal
detection theory was the primary methodological tool used for the
analysis of Tasks Three, Four, and Five.
Error detection was modeled
as a signal detection process.
The decision made by the subject in an error detection task
is thought to depend upon two factors:
(1) the sensitivity of the
subject to the signal strength (d'), and (2) whether or not the
observation exceeds a criterion adopted by the subject in a given
situation.
The decision a student renders in making a response will
have one of four possible outcomes:
the observer tay say "yes" or
"no" and may in each case by correct or incorrect.
The decision
outcome, therefore, nay be a hit, saying error when an error is
present; a miss, saying that an error is not present when an error is
98
present; a correct rejection, saying that no error is present when an
error is not present; or a false alarm, saying error when an error is
not present.
These four outcomes are interdependent.
When monitoring, the student is presumed to have to decide
whether a particular item is in error or not.
He makes that decision
as if he were to (1) observe the item and relate it to what he knows;
(2) generate an internal scalar variable monotonic with the probability
that the item is in error given both the observation and what he
knows; and (3) decide it is in error if the internal variable is
larger than or equal to a specific criterion level, or decide it is
not in error if it is less than that criterion.
Task One:
Creative Writing
Results of F and ^-tests showed significant differences between
the variances and means on the measures of errors, errors detected,
percent errors detected, and nonerrors detected for the learning
disability and the non-learning groups.
The learning disability
group made significantly more errors than the non-learning disability
group, but their performance on detection of errors and percent of
errors detected was significantly poorer than the non-learning
disability group.
While the variance and mean differences between
the two groups were significant In nonerrors detected, the absolute
number of errors detected in each instance was so s&all that it was
not considered to be a meaningful index in this task.
99
Task Two:
Editing
Results of F and t-tests showed significant differences between
the means and variances on the measures of errors detected, percent
errors detected, nonerrors detected and percent errors corrected for
the learning disability and the non-learning disability groups.
No
significant difference was found between the groups on the errors
corrected measure.
Task Three and Four:
Spelling
For the Yes-No Spelling Task, a significant difference was
found between the two groups on their detectibility of errors (d').
Results showed that the learning disability group could not tell the
difference between errors and nonerrora and their performance was not
much better than chance.
The non-learning disability group demonstrated
good detectibility of errors.
Measures of criteria were not computed
for this task because an analysis of the raw data indicated that the
signal detection model broke down for several of the cases in the
learning disability group.
Therefore, a measure of the proportion
of error responses p(e) wa6 computed. A jt-test applied to the p(e)
scores for the two groups showed no signlficaut diJlcrencc on this
measure.
The aean p(e) values for each group ic£lcc;ed an unwillingness
to say "error" unless a high degree of certainty exloted.
The Two-Alternative Forced-Choice Spelling task (2AJ'C) was
presented to both groups to test the internal cuaoioteitcy ui the
signal detection codel.
A Spearoan rank, order correlation dune on the
d' values froa the Yes-No Spelling Task and it via. ttue 1'Al'C Si/clling
100
Task.
The resulting correlation of .85 indicated that the model can
be applied to both yes-no and 2AFC data and that similar measures of
detectibility can be derived with either type of task.
Task Five:
Vocabulary
A significant difference was found between the two groups on
their detectibility of errors in this Vocabulary Task.
The non-learning
disability group was better at detecting errors in vocabulary usage
than the learning disability group.
A significant point however, is
that the detectibility evidenced by the learning disability group on
this task was considerably better than their detectibility of errors
on the spelling tasks.
This difference in performance may be explained
by a well-documented characteristic of the learning disability group,
namely, that of normal intelligence.
Methodological Implications
Bayesian Statistics
This study and DeRuiter's (1973) demonstrated the effectiveness
of applying the Bayesian procedure to different tests at different
age levels for the identification of learning disability.
In each
case, a relatively ssall aaount of data was needed to produce a high
probability ol identifying the condition.
The attitude of "the core
the better" often characterizes the philosophy of hov cany tests to
give to student* tor the Identification of learning disability.
In
that the bayealdti approach combines information in a weighted fashion,
it provides a
fur answering a cocjaon probleo in identification
101
of handicapped populations; namely, how much data are necessary for
successful identification?
The question of what constitutes the best
number and combination of measures is of crucial importance in developing
an economical and efficient identification procedure.
The test measures used in this study effectively discriminated
learning disability from non-learning disability.
These should be
cross-validated on learning disability and non-learning disability
students other than those on whom the data were gathered.
They should
also be validated on other handicapped groups such as the mentally
retarded and the emotionally disturbed to enhance their worth as
discriminators of learning disability students.
Aside from giving some alternatives to identification questions,
the Bayesian procedures have provided a means of systematically
studying the characteristics which differentiate learning disability
from non-learning disability.
This study, in addition to those of
Wissink (1972), DeRuiter (1973), Johnson (1973), and Kaiser (1974),
utilized a particular outline of component disabilities and isolated
some pertinent characteristics of learning disability.
Signal Detection Theory
The modeling of error detection aa a signal detection process
for the analysis of performance seems justified.
One of the obvious
advantages of signal detection theory is that decisions can be analyzed
according to two factors:
decisions.
measured.
sensitivity to signal and criteria for
In addition, the interaction of these factors can be
Such a model should be helpful In determining the effects
102
of nonprocess factors such as motivation and attitude on performance
and the interaction of these factors with learning disability per se.
A signal detection model can be applied in clinical or class­
room settings in that it is relatively easy to work with and does
not demand detailed calculations and the analysis of results is
straightforward.
Performance can be charted on scatter diagrams or
relative operating characteristic (ROC) curves and analyzed by visual
inspection.
Statistical analyses are not required.
By considering
all possible options for an answer (hit» miss, false alarm, or correct
rejection), the teacher can get a more complete understanding of a
student's or group's performance than by merely considering one
measure such as the number of items incorrect.
Signal detection theory provides a means of studying changes
in performance by systematically varying factors such as signal
strength, likelihood of errors, and the costs and rewards of giving the
correct answer.
For example, signal strength can be varied by either
increasing or decreasing the signal or increasing or decreasing the
noise.
Signal detection theory can be used with yes-no data, alternativeforced-choice data and rating scale data, but it has limited application
with tasks where no specific interval in which observations occur can
be specified.
The investigator experienced considerable difficulty
in designing tasks which met the task specifications for the signal
detection model as well as meeting age and curriculum criteria.
Caution
must therefore be exercised to apply this oodel only to data which meets
the limitations of the model.
103
Concluding Statement
The development of viable research methodologies for the field
of learning disability is still in its infancy.
However, it is possible
that continued application of traditional approaches is not necessarily
the most productive. The efficacy of the two approaches outlined
above remains to be determined in many areas, but these seem to offer
some potential for a new approach to research questions in the field.
Along with the need for new methodologies is that of a conceptual
framework in order for research to be done in a systematic and logical
fashion.
The model of learning deviance as suggested by Kass (1973)
has been the source of theory for this research study.
Practical Implications
Implications from Test Data
The tests used in this study were shown to be eflective instru­
ments for identifying learning disability adolescents. The tests
were:
the Reading Comprehension and Mathematics tests from the Feabody
Individual Achievement Test (Dunn and Markwardt, 1970), the Blending
test of the Stanford Diagnostic Reading Test (Karlsen et al., 1966),
and the Picture Story Language Test (Myklebust, 1965).
Although validation is needed, these tests could provide a
core battery for screening purposes at the high school level.
Each
of the tests in this battery takes approximately five to 15 minutes to
administer and the battery need not be given in one session.
Thus,
screening can be accomplished without drastic adjustments in the
regular classroom activities.
104
Five of the measures (the five scores from the Picture Story
Language Test) were also used by DeRuiter (1973).
In each study,
these measures were ranked among the highest in diagnosticity suggesting
that a test which taps written ability should be included in screeing
batteries at the elementary and high school levels.
The Picture
Story Language Test is particularly attractive because it can be
administered in group as well as individual settings and yields a
wealth of information for screening purposes.
The relative homogeneity of the learning disability population
that was noted in the sequential analysis of test data suggests that
research questions need not be approached through the nomothetic method.
Further, specialized curriculum, if validated, could be used with more
confidence.
Implications from Task Data
The tasks (Creative Writing Task, Editing Task, Yea-No Spelling
Task, 2AFC Spelling Task, and Vocabulary Task) were shown to be
effective in differentiating learning disability from non-learning
disability.
These can be used by both regular and special class
teachers to advantage.
Regular class teachers can use thco as an
Informal means of initially referring youngsters to special services
for in-depth diagnosis.
Special class teachers can center reaediation
around them as well as using them as a Beans of analyzing a student's
performance and progress.
These tasks convey data concerning a student's level of perfor­
mance, specific areas of weakness, and respond injj strategics in
105
detecting errors.
For example, the Creative Writing Task yields
measures of a student's facility in written expression, vocabulary
usage, error detection, error types.
Indications of response strategy
can be inferred from a signal detection analysis.
Task relevance is
enhanced when age-related curriculum requirements are tapped.
The tasks are not standardized, as are formal test instruments,
and therefore offer more flexibility to the teacher in mode of
application.
The tasks can be used primarily for screening, for
remediation, or for a combination of screening and remediation.
The
tasks can be redesigned for a specific student or group and thus
avoid problems of bias found in tests standardized on restricted
samples.
While all tasks successfully differentiated between the two
groups, the Yea-No Spelling Task was the best discriminator because
there was virtually no overlap of distributions.
This task even
achieved better separation than any of the tests adcinistered in the
selection procedure.
Standardisation of this task night be warranted
for screening ^r diagnostic purposes.
APPENDIX A
QUESTIONNAIRE AND
PROCESS OUTLINE
iu6
107
QUESTIONNAIRE INSTRUCTIONS
Purpose of the Study
At the present time there is no one instrument which accur­
ately allows us to identify the existence of all learning disabili­
ties. It is possible, however, to identify learning disabilities
through clinical diagnosis. At the same time, clinical diagnosis
presents problems when it becomes necessary to screen a large number
of referrals for public school services. These problems relate to
economics (clinical diagnosis is expensive), to personnel (there are
not enough clinicians to do the job), and to administrative implemen­
tation (there is no economical and efficient procedure for screening).
These problems may be alleviated by analyzing clinical diag­
nosis in such a way that identification of learning disabilities can
be separated from the more intensive diagnosis of deficits. Such a
division of clinical diagnosis is suggested as follows: (1) subjec­
tive Judgment for identification of learning disabilities leading to
placement in the special learning disability services, and (2) indepth individual diagnosis leading to remediation plans and programs.
This study will be concerned with the first aspect—subjective
clinical judgment.
This study will explore a technique for quantifying the judg­
ment that learning disabilities exist when certain component dis­
abilities coabine to produce a handicap in learning. Each component
disability by itself is not sufficient for the identification of
learning disabilities. For example, a memory deficit night be present
in a child without learning disabilities. Usually, several component
disabilities must be combined to establish a high probability that
the condition of learning disabilities is present. Independence or
non-independence of the component disabilities cannot be assue-cd.
The teclinique to be explored in this study is called "Bayesian
revision of subjective probabilities." It permits expert opinion,
which is given in the form of estie-ates, to stow <x prubab 11 ibtic re­
lationship between a coeponent disability (such as Ee&ory) and the
existence of learning disabilities. An application ot fcayes' Theoren
provides a fcathe&atical eieans for estiEiating the probability ut the
existence ot learning disabilities when cosap^neut disabilities are
expressed in livelihood estimates.
This study will (1) define a set of conp-oucnt disabilities
which saay be related to learning disabilities, (-) collect likelihood
ratios tor ea^h exponent disability troei experts in the t leid ui
learning disabilities, and (J) apply the "is-ayrsiaii revision
sub­
jective probabilities" lectiniquc to the llk.cllhi.-u>! estimates !.!
purposes o! deve lv/p in£ a procedure ior the identification ui ^r.ildreu
with learning disabilities.
108
The purpose of this questionnaire is to gather clinical esti­
mates for component disabilities which may or may not be related to
learning disabilities. If research studies in this area were conclu­
sive, clinical estimates would not need to be gathered. The inclusion
of the selected component disabilities should not be taken as evidence
that they are factors exclusively related to learning disabilities.
An outline format has been used as a framework for this instrument.
The major headings are central processes and are defined for your
convenience in estimating percentages.
Game Rules
You are requested to follow these game rules when considering
the component disabilities:
Please use the definition which is given for each component
disability.
Base your estimates on your experience and subjective intuition.
Component disabilities are assumed to be age-related and within
the K-12 school population.
Assume integrity of peripheral senses of the children with learn­
ing disabilities.
As you consider each component disability, conceive each as being
severe enough by itself to interfere with learning.
Directions for Completing the Questionnaire
1.
2.
Complete directions a, b, and c before completing direction two.
a.
Read the definition for each component disability.
b.
In the blank labeled L.D. write your eutitaate of the per­
centage of children with learning disabilities who arc
likely to have this cueponent disability.
c.
In the blank labeled Son I..D. write your estimate of the
percentage of children vichuut learning disabilities whu
are likely to tiave this tuiponent disability.
After co&pleting direction une,
over the questionnaire again
for the purpose of noting relat ior.bhips aeoug the component
disabilities.
109
a.
Scan the definitions of the component disabilities again.
b.
Based on your clinical experience, if you think that any
component disability is related to any other component dis­
ability write the number(s) of the related component dis­
abilities in the appropriate box on the answer sheet for
direction two. For example, if you estimate components 1
and 2 are related to 3, write 1 and 2 in the box numbered
3 and 3 in the boxes numbered 1 and 2, etc.
SAMPLE BOXES:
If you think that a certain component disability is not
related to any other disability, please leave the appro­
priate box blank.
Examples
As an example for direction one, consider a hypothetical
component disability such as:
Toe tapping deficit—an impairment in the child's
ability to respond quickly and consistently in
toe tapping activities.
LD
% Non LD
%
After reading the definition, you are asked to consider the
learning disability population you have observed in your clinical
work. What percentage of this population do you estimate exhibit a
"toe tapping" deficit severe enough to be a handicap in learning?
For our example, let us assume this estimate to be x% of the learning
disability population.
Now consider the same definition and think about the normal
population, Including all other handicaps. What percentage of this
reaaining population do you estimate exhibit a "toe tapping" deficit?
110
For our example, let us assume an estimate of y%. Please record your
answers on the questionnaire as follows:
LD
% Non LD
%
While completing the estimates for the component disabilities,
the thought may occur to you that one component disability may lead
you to expect finding an associated component disability. Therefore,
as an example for direction two, consider the hypothetical "toe
tapping" deficit defined above. If you have clinically observed this
hypothetical deficit, you might also expect to find a related "pattycake" deficit. If you think these hypothetical deficits are directly
related, you would place the number for "toe tapping" in the "pattycake" box and the number for "patty-cake" in the toe tapping box.
PLEASE NOTE:
1. The non-learning disability population, for the purposes of
this study, includes all normal as well as all exceptional children
other than children with learning disabilities.
2. In some cases the percentage for the non-learning
population may be higher than for the learning disability
The inclusion of the component disabilities found in this
does not reflect a necessary relationship to the learning
population.
3.
disability
population.
questionnaire
disability
The percentages need not add to 100%.
4. If you estimate a certain component disability is found equally
in both populations, record an equal percentage for both categories.
5.
There are no incorrect answers.
6. You may find it helpful to separate the pages when completing
direction two, and spread them out for ease in filling out the answer
sheet.
THANK YOU FOR YOUR COOPERATION. Please discard the instruc­
tions and return the questionnaire and answer sheet in the enclosed
self-addressed envelope.
QUESTIONNAIRE
Corrine E. Kass and John F. Wissink
Sensory Orientation—the process by which the child shows a
physiological or functional orientation of the sensory recep­
tors to the states of (a) arousal, (b) body awareness, (c) dis­
crimination of sensory information, and (d) sensory coordination.
A.
Arousal means the excitability of the
sensory receptors.
1.
2.
3.
A.
B.
Attention deficit—an impairment
in the child's ability to focus
on specific sensory input.
LD
X
Non LD_
Hyperexcitability—an impairment
in the child's ability to control
the arousal of his sensory re­
ceptors.
LD
X
Non LD_
Hypoexcitability—an impairment
in the activation of the child's
sensory receptors.
LD
X
Non LD_
Perseveration—an impairment in
the child's ability to switch
focus—i.e., the termination of
activation of certain sensory
receptors and in the subsequent
arousal of other sensory recep­
tors.
LD
X
Non LD
Body balance deficit—an impairment
in the child's ability to main­
tain equilibrium.
LD
X
Non LD
Z
Spatial deficit—an impairment
in the child's ability to relate
to two or more objects in space.
LD
X
Non LD
2
Temporal deficit—an iepairment
in the child's ability to locate
himself within a tiae perspec­
tive.
LD
X
Non LD
Z
Body Awareness means the recognition
of the spatial and temporal location
of sensory input.
5.
6.
7.
8.
9.
10.
Visual pursuit deficit—an impair­
ment in the child's ability to
follow visual stimuli.
LD
X
Non LD
Auditory direction deficit—an
impairment in the child's ability
to locate the origin of auditory
sensory input.
LD
X
Non LD
Maturational lag—an impairment
in the development of the child's
body awareness system.
LD
X
Non LD
Auditory discrimination deficit—
an impairment in the child's
ability to note difference#
within the auditory sensory
system.
LD
X
Non LD
Visual discrimination deficit—
an impairment in the child's
ability to note differences
with the visual sensory system.
LD
X
Non LD
Kinesthetic discrimination defi­
cit—an Impairment in the child's
ability to note differences
within the kinesthetic (e-uacle
sensation) sensory systcea.
LD
X
Non LD
Tactile discrininatlon dctlcit-an Impairment In the child's
ability to note dltlciciitco
with in the tactile (touch) acn»ory systea.
LD
Z Hon LD
Lti
t !ian LD
Discrimination of sensory information
means the ability to note differences
within any one sensory system.
11.
12.
13.
14.
Sea«>ury Coordination steams the inte­
gration of tWO or B«Jre BcUoujy o>otcajj.
15.
Vibual-luipt lc (iKiricethct
avA
tactile) coordination dcti^n-*iv l&palrmciu In tkc «.M1 -' o
ability to receive aiui aeao^laic
ifttor&atlon iroa visual *a-4 Lac­
tic benaory sy6tciu>.
113
16.
17.
18.
II.
Auditory-visual coordination
deficit—an impairment in the
child's ability to receive and
associate information from the
auditory and visual sensory
systems.
LD
X
Auditory-haptic coordination
deficit—an impairment in the
child's ability to receive and
associate information from the
auditory and haptic sensory
systems.
LD
% Non LD_
Auditory-visual-haptic coordina­
tion deficit—an impairment in
the child's ability to receive
the same information from the
auditory, visual, and haptic
systems.
LD
X
Non LD
Non LD_
Memory—The process by which the child shows (a) immediate re­
trieval of sensory information, (b) storing of sensory im­
pressions through rehearsal, and (c) delayed retrieval of
organized material.
19.
20.
21.
22.
Visual short-term memory span
deficit—an impairment in the
child's ability to retrieve
imnediately a match of the
visual stimulus input.
LD
X Non LD
X
Auditory short-term memory span
deficit—an impairment in the
child's ability to retrieve
ieaaediately a match of the
auditory stimulus input.
LD
Z
Non LD
X
Rehearsal deficit—an impairment
in the child's method of storing
the nacch of the sensory input
for later recall.
LD
X Non LD
X
Long-tern eteaory deficit--an
lapairaent in the child's ability
to recrleve scored nacerial ac a
delayed clae afcer stimulus
input.
LD
2 Non LD
X
114
III.
Reception—the process by which meaning is attached to external
or internal stimuli without being aware of the specific stimuli.
23.
24.
25.
26.
27.
28.
29.
IV.
Visual figure-ground deficit—
an impairment in the child's
ability to gain meaning from
the appropriate visual stimuli
while ignoring inappropriate
visual stimuli.
LD
% Non LD
Listening comprehension deficit—
an impairment in the child's
ability to gain meaning from the
appropriate auditory stimuli.
LD
% Non LD
Visual closure deficit—an im­
pairment in the child's ability
to gain meaning from incomplete
visual stimuli.
LD
% Non LD
Auditory closure deficit—an
impairment in the child's
ability to gain meaning from
incomplete auditory stimuli.
LD
Z
Non LD_
Reading comprehension deficit—
an impairment in the child's
ability to gain meaning from
the printed page.
LD
X
Non LD_
Mathematical conprehension defi­
cit—an impairment in the child's
ability to gain meaning from the
appropriate quantitative symbols.
LD
X
Non LD_
Social comprehension deficit—an
impairment in the child's ability
to gain eeaning frue the appro­
priate interpersonal stimuli.
LD
% Non LD_
Expression—the process by which meaning is communicated.
30.
31.
Oral expression deficit—an im­
pairment in the child's ability
to coenunicatc leaning through
the spoken word.
LD
X
Writing deficit — an iepaiment
in the child's ability to coanunicate taeaning through the
written word.
LD
t Non LD
Non LD_
%
115
32.
33.
34.
V.
Body language deficit—an impair­
ment in the child's ability to
communicate meaning through ges­
tures and other physical move­
ments.
LD
% Non LD
Quantitative deficit—an impair­
ment in the child's ability to
communicate meaning through a
mathematical system.
LD
% Non LD
Affect deficit—an impairment in
the child's ability to communi­
cate meaning through appropriate
emotional reaction.
LD
% Non LD
%
Integration—the process by which separately learned components
from the processes of sensory orientation, memory, reception,
and expression are unified and compacted into one internal rep­
resentation or gestalt (the whole is more than the sum of its
parts).
35.
36.
37.
38.
39.
Visualization deficit—an impair­
ment in the child's ability to
synthesize sensory inputs into
visual representations.
LD
% Non LD_
Sound blending deficit—an im­
pairment in the child's ability
to synthesize sounds into an in­
ternal representation.
LD
X Non LD_
Prediction deficit—an impair­
ment in the child's ability to
recognize a match between his
performance and his internal
representations.
LD
X Non LD_
Monitoring deficit—an impair­
ment in the child's ability to
recognize dissonance between
his performance and his internal
representation.
LD
X
Non LD_
Visual speed or perception
deficit—an impairment in the
child's ability to respond
quickly and consistently froa
internal visual representations.
LD
X
Non LD_
116
40.
Question:
Auditory speed of perception
deficit—an impairment in the
child's ability to respond
quickly and consistently from
internal auditory represen­
tations.
LD
% Non LD
%
What percentage of school-aged children (K-12) have learning
disabilities?
% (Please do not specify a range).
APPENDIX B
SAMPLE SUMMARY SHEET
Case number_
Age of child
Grade
Sex
Achievement Scores
Academic
Area
Test
Scaled
Score
Grade
Score
%ile
Age Time of testing
Score
A p,e
Grade
Discr epancy
Age Crade
Psychological test scores
Test
Subtest
Raw
Score
Scale
Score
Age
Score
117
Zile
Time oi testing
Age
Grade
118
Test
Subtest
Raw
Score
Scale
Score
Age
Score
Xile
Time of testing
Age
Grade
Reason for referral
Clinical impressions
Remedial procedures
Results of remediation
Other pertinent information (school, medical, etc.)
APPENDIX C
RAW TEST SCORE DATA
Appendix C presents the raw data from the tests given to the
sample groups.
The data for the samples is presented on separate
pages, with the learning disability sample first.
The variable
numbers correspond to the variables as numbered below.
1.
The Reading Comprehension subtest from the Peabody
Individual Achievement Test (PIAT).
2.
The Abstract-Concrete score from the Picture Story
Language Test (PSLT).
3.
The Blending subtest from Che Stanford Diagnostic Reading
Test.
A.
The Mathematics subtest from the PIAT.
5.
The Syntax Quotient from the PSLT.
6.
The Total Sentences score from che PSLT.
7.
The Words score from the PSLT.
8.
The Words per Sentence score fron the I'SLT.
119
120
Table C.l.
Case
Number
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
JO
31
32
33
34
35
36
LD group raw test score data.
Variable
1234
17
2
16
5
26
13
20
15
23
18
31
10
25
19
9
28
24
16
15
2
8
3
28
10
1
6
14
.'0
0
61
48
55
46
57
48
62
47
52
50
57
49
51
50
51
45
54
48
45
50
51
51
60
67
45
56
53
20
1
•;c
49
o2
7
7
1
a
4o
1
4J
7
10
60
31
67
39
49
46
53
42
55
48
54
51
48
54
46
68
53
56
59
53
39
41
50
58
19
41
45
62
42
55
44
46
18
9
18
7
10
6
15
15
10
7
14
18
12
20
14
15
16
7
15
7
9
7
8
7
0
7
7
14
7
19
15
lu
46
47
20
29
20
60
49
J9
56
95
88
99
100
95
90
96
86
96
89
93
95
89
92
93
96
91
100
95
96
88
86
85
88
0
85
93
92
91
92
85
89
88
4
3
5
1
2
6
6
5
5
3
4
5
5
4
5
2
7
4
2
5
4
2
3
3
0
8
1
8
9
5
5
5
7
81
54
137
9
48
54
70
99
54
39
50
79
90
66
46
51
116
85
45
84
58
38
45
36
0
67
14
12 3
143
50
8
20.2
18.0
25.4
9.0
24.0
9.0
11.6
19.8
10.8
13.0
12.5
15.8
18.0
16. 5
9.2
25.5
16.5
21. 2
22.5
16.8
14.5
19.0
15.0
12.0
OO.0
S.4
14.0
15.3
I ' j. i
10 . 'J
u.ti
*
69
43
49
91
c
J
88
8.c
12.2
17 . c
Iw
1
91
5
2
42
• vl
8. 4
121
Table C.2.
Case
Number
1
2
3
A
5
6
7
8
9
10
11
12
13
1A
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
NLD group raw test score data.
Variable
12345678
78
58
57
63
68
60
61
6A
61
59
65
62
53
7A
72
61
65
58
68
59
66
68
60
66
67
65
62
67
70
73
69
72
7A
57
47
64
22
23
7
10
19
21
8
22
18
20
16
22
18
22
18
19
20
18
16
23
19
17
22
18
22
18
24
18
19
23
16
19
23
19
23
16
35
33
26
27
34
36
22
33
29
29
36
35
30
36
36
31
35
35
19
36
3A
28
35
33
31
33
35
33
31
36
35
31
36
28
34
27
73
58
6A
5A
67
60
61
A5
55
66
63
53
68
73
66
53
60
65
50
69
56
69
59
65
78
69
51
63
7A
76
76
79
73
60
60
61
97
99
100
93
97
9A
97
9A
98
92
100
97
97
97
97
98
100
97
98
95
98
97
99
96
98
100
98
96
100
98
100
06
100
98
96
99
1A
19
5
7
6
7
7
13
9
5
9
11
10
13
7
7
9
12
A
5
6
9
16
10
8
6
11
15
5
8
8
7
8
5
3
9
168
275
61
113
128
105
106
213
1A2
50
136
160
10A
1A5
13A
160
118
206
51
67
129
126
299
121
123
115
150
15A
104
170
100
124
202
114
43
121
12.0
1A.5
12.2
16.1
21.3
15.0
15.1
16.3
15.7
10.0
15.1
1A.5
10.A
11.1
19.1
22.8
13.1
17.2
12.7
13.A
21.5
1A.0
18.6
12.1
15.3
19.2
13.6
10.2
20.8
21.2
12.5
17.7
25.2
22.8
14.3
13.4
APPENDIX D
m AND n VALUES
Appendix D presents m and n values, which are parameters of
the beta distributions.
The variable numbers, 1-8 correspond to the
tests listed in Appendix C.
Table D.l.
LD group
NLD group
Table D.2.
LD group
NLD group
m values
Variable
4
1
2
3
3.532
15.303
2.139
5.058
1.358
6.033
5
23.260
2.639
13.671 62.415
6
7
8
3.869
4.682
2.703
3.478
3.300
8.518
6
7
8
n values
Variable
4
1
2
3
4.461
6.679
2.723
1.656
2.141
.748
14.967
4.366
122
5
.313 34.871
1.673 17.936
12.611
5.582
4.447
9.774
APPENDIX E
LIKELIHOOD RATIOS FOR EACH SUBJECT
Appendix E presents likelihood ratio (LR) values for each
subject for the four tests administered to the research samples. The
four tests yielded eight sets of scores (the Picture Story Language
Test yielded five scores, all others yielded one).
LR values of less
than .001 and more than 10,000 have been rounded to those figures.
The data for the samples is presented on separate pages, with the
learning disability sample first.
The variable numbers, 1-8 correspond
to the tests listed in Appendix C.
123
Table E.l.
Case
Number
37
38
39
40
41
42
43
44
45
46
47
46
49
50
51
52
53
54
55
56
57
56
59
60
fcl
62
63
64
65
66
Likelihood ratios for LD group.
1
2
3
Varia
4
5
6
7
8
.44
10,000.00
.15
507.91
7.50
21.60
2.25
114.22
1. 33
10.50
1.72
4.00
10.50
1.72
21.60
.13
2.25
1.04
.54
2.25
507.91
182.95
5.44
.66
10,000.00
182.95
31.80
.30
114.22
1.33
.43
7.94
.43
18.75
5.45
31.14
1.08
1.08
5.45
18.75
1.47
.43
2.75
.22
1.47
1.08
.80
18.75
.80
18.75
7.94
18.75
11.94
18.75
10,000.00
16.75
18.75
1.47
.22
18.75
15.54
10,000.00
22.16
9,376.51
.87
71.07
5.72
32.07
2.23
11.03
.15
287.39
1.20
7.91
495.67
.45
1.63
22.16
32.07
10,000.00
904.29
10,000.00
.45
287.39
10,000.00
3,820.08
47.24
.87
3,820.08
5.72
.51
5.92
2.21
6.99
1.46
5.92
.37
6.47
3.66
4.78
1.46
5.36
4.21
1.72
4.21
7.45
2.65
5.92
7.45
4.78
4.21
4.21
.68
.05
7.45
1.81
3.14
.68
5.36
6.99
.51
15.02
.39
.39
.51
5.02
.37
48.14
.37
8.61
1.15
.51
8.61
1.83
1.15
.37
3.00
.39
.51
.37
15.02
48.14
88.19
15.02
10,000.00
88.19
1.15
1.83
3.00
1.83
3.42
6.71
1.82
38.27
14.34
.99
.99
1.82
1.82
6.71
3.42
1.82
1.82
3.42
1.82
14.34
.54
3.42
14.34
1.82
3.42
14.34
6.71
6.71
98.32
.30
38.27
.30
.16
1.82
1.50
4.02
.19
43.56
5.07
4.02
2.22
.79
4.02
7.32
4.69
1.61
1.09
2.57
5.49
4.51
.43
1.30
5.71
1.35
3.46
7.64
5.71
8.33
101.33
2.48
27.88
.33
.15
4.69
.75
.62
2.81
2.15
1.69
2.15
1.03
.71
1.24
.80
.86
.62
.62
.61
2.00
2.93
.61
.87
1.13
.61
.67
.66
.64
.95
10,000.00
2.71
.70
.63
.63
1.54
Table E.l.
Case
Nur-ber
67
68
69
70
72
72
Likelihood ratios for LD group—Continued.
1
47.70
21.60
10. 5)0
14.94
10.000.00
10.000.00
2
.31
1.06
18.75
18.75
7,466.17
18.75
3
287.39
1,772.64
1,772.64
904.29
9,376.51
2S7.39
Variable
4
5
5.36
.37
6.99
6.99
7.06
8.62
88.19
8.61
15.02
3.00
.39
3.00
6
7
1.82
1.82
3.42
1.82
38.27
1.82
2.31
6.20
4.88
1.17
161.15
6.46
8
.72
2.50
.91
.61
1.477.41
2.71
ro
Tabic E.2.
Case
Number
Likelihood ratios for NLD group.
12
.10
.01
.05
.87
.63
.03
.001
3.04
.05
.32
.32
.001
.01
.22
.001
.001
.15
.01
.01
7.91
.001
.03
.45
.01
.05
.15
.43
.02
.43
.01
.05
.31
.06
.001
1
2
3
4
5
6
7
e
9
10
11
12
13
14
15
16
17
16
19
20
21
22
.13
.66
.63
.26
.13
.44
.36
.22
.36
.54
.19
.30
2.25
.10
.10
.36
.19
.66
.13
.54
.17
.13
.10
.06
16.75
5.45
.31
.15
11.94
.10
.43
.22
.60
.10
.43
.10
.43
.31
.22
.43
.80
.06
.31
.59
23
24
;s
.44
.17
.15
.10
.43
26
27
:t
29
.19
30
.10
. 30
.15
.11
3
.05
.15
Variable
4
.001
1.15
.18
2.65
.05
.68
.51
7.45
2.21
.08
.27
3.14
.03
.001
.08
3.14
.68
.12
4.78
.02
1.81
.02
.90
.12
.001
.02
4.21
.27
.001
.001
5
6
7
8
.29
.39
.39
1.15
.29
.75
.29
.75
.28
1.83
.39
.29
.29
.29
.29
.28
.39
.29
.28
.51
.28
.29
.39
.37
.28
.39
.28
.37
.39
.28
.01
.001
1.82
.54
.99
.54
.54
.01
.16
1.82
.16
.05
.09
.01
.54
.54
.16
.03
3.42
1.82
.99
.16
.001
.09
.30
.99
.05
.001
1.82
.30
.05
.001
3.09
.48
.27
.64
.61
.01
.16
4.69
.20
.08
.66
.14
.22
.08
.40
.01
4.51
2.48
.26
.29
.001
.35
.33
.44
.12
.10
.66
.05
.95
.67
.91
.61
.88
.64
.64
.61
.62
1.54
.64
.67
1.37
1.15
.67
1.21
.79
.61
.84
.75
.92
.70
.64
.93
.63
.67
.74
1.45
.81
.87
IsHe t. r .
Likelihood ratios for KLD group—Continued.
Case
Kun.l>ci
2
2
31
j2
33
.i:
.20
.20
.31
34
.31
35
.63
14.94
36
.22
.60
.60
.06
.06
Variable
34
5
6
7
.01
.15
.001
.45
.03
.63
.39
.37
.39
.28
.37
.39
.001
.001
.001
.68
.68
.51
.30
.54
.30
1.82
6.71
.16
.76
.32
.01
.46
6.20
.35
8
.86
.61
2.59
1.21
.68
.75
APPENDIX F
RAW TASK DATA
Appendix F presents the raw data from the five monitoring tasks
given to the research samples.
The data for the samples Is presented
on separate pages, with the learning disability sample first.
The
variable numbers correspond to the variables as numbered below.
1.
Task One:
Creative Writing—errors.
2.
Task One:
Creative Writing—errors detected.
3.
Task One:
Creative Writing—non-errors detected.
4.
Task Two:
Editing—errors detected.
5.
Task Two:
Editing—non-errora detected.
6.
Task Two:
Editing—errors corrected.
7.
Task Three:
Spelling (Yes-Sio)— hits (e|E).
8.
Task Three:
Spelling (Yes-No)—false alarms (e|C).
9.
Tank Four:
Spelling (2AFC)--hies (e jE).
10.
Task Five:
Vocabulary--nu£tber of pairs starke<i "1" which were
Byaunytui {1 j S).
11.
Task Five:
Vucabulary--nusa.ber u£ paira «e*»rke<d " 2 " which were
syiwnya-s <21 S).
12.
Task Five:
t y B H i u y v u i (
13.
Task Five:
Vo«:ab*iiai y—nuaiber of jxtr la sin i Veil "3" which were
3 .
Vucabuiaiy—auJibcf ut Jjalto &a(kc*i "i" which Were
oyjiiufiyma (4 IS).
1J«
129
14.
Task Five:
Vocabulary—number of pairs marked "5" which were
synonyms (5|S).
15.
Task Five:
Vocabulary—number of pairs marked "1" which were
not synonyms (l|N).
16.
Task Five:
Vocubulary—number of pairs marked "2" which were
not synonyms (2|N).
17.
Task Five:
Vacabulary—number of pairs marked "3" which were
not synonyms (3|N).
18.
Task Five:
Vocabulary—number of pairs marked "4" which were
not synonyms (A j N).
19.
Task Five:
Vocabulary—number of pairs marked "5" which were
not synonyms <5|N).
Table F.l.
C»«e
Number
37
38
40
41
42
43
44
45
4()
47
4P
49
Hev ta«V data lor LD group.
1
•5
3
4
5
6
7
8
40
20
15
10
33
16
11
10
20
14
40
16
39
40
11
59
0
4
0
1
2
3
0
1
4
0
2
5
1
0
0
7
0
21
5
7
23
22
22
8
22
5
17
12
21
13
15
23
6
23
2
0
0
0
6
7
5
14
4
4
20
12
19
4
19
4
12
10
14
6
8
23
7
16
5
4
3
7
14
12
4
10
5
6
12
12
4
11
1.1
8
1A
13
12
11
14
11
10
8
12
13
4
11
7
16
15
12
11
7
16
12
12
13
6
11
16
13
12
11
13
14
10
6
12
9
11
13
7
9
9
9
12
5
12
8
6
12
9
12
7
1C
12
8
10
7
7
6
12
:•
40
16
6
0
1
12
0
4
9
6
7
ie
5
5
20
0
21
2
14
;>c
'•7
:**
10
ii
4
*>9
17
20
p
12
.*>0
51
!>:
.'-3
54
B
(.0
:<
(1
30
39
(
(3
(5
CI
rt
31
4
(7
33
IS
29
10
21
2
12
0
12
10
2
0
4
0
7
7
16
14
5
12
0
9
3
2
2
0
10
14
22
5
t
2
6
10
6
2
2
7
4
11
11
2
11
4
3
6
6
H
1
3
4
7
4
3
8
7
7
10
4
Variable
9
10
37
23
23
3A
25
37
29
35
23
28
33
32
30
15
35
25
31
35
17
28
24
33
30
17
23
25
31
34
25
17
9
10
5
10
11
10
8
7
10
11
11
13
2
9
17
12
1A
1A
7
8
12
15
19
7
19
8
9
16
11
7
11
12
13
14
15
16
17
18
19
A
3
A
1
0
2
A
1
3
0
7
A
8
2
0
6
1
0
8
A
6
2
2
8
0
A
A
1
0
8
7
7
8
8
5
1
5
2
7
8
5
6
7
3
2
A
5
6
6
5
A
3
3
6
A
6
2
0
5
6
3
1
A
1
2
5
2
3
1
0
1
1
5
5
1
1
0
1
2
2
0
1
0
2
1
6
3
3
2
2
2
A
A
5
7
7
6
12
A
6
1
1
2
6
5
2
5
A
2
6
3
A
1
2
2
1
7
5
7
2
0
A
A
0
5
1
0
1
A
3
1
3
0
1
1
6
1
0
A
2
0
1
3
3
2
3
A
0
A
0
A
5
2
A
1
A
5
0
3
0
1
0
5
7
A
6
7
3
1
5
0
A
10
5
5
6
5
1
5
6
6
2
5
5
1
A
2
1
2
3
1
3
2
5
A
3
2
1
3
0
A
A
1
A
5
8
1
0
6
0
3
A
0
6
1
1
A
1
6
5
1
1
A
12
12
6
15
16
16
18
20
12
8
12
10
9
9
23
7
18
5
13
18
7
21
15
13
21
12
15
20
16
13
6
1
3
1
7
1
0
3
1
1
1
1
2
2
2
5
1
Table F.l.
Raw task data for LD group—Continued.
Case
1
2
3
4
5
6
7
8
70
71
53
31
33
0
0
12
36
22
12
15
12
9
9
6
8
13
9
4
5
4
3
4
5
10
10
12
10
9
13
14
10
Nus-ber
f>9
6
3
Variable
9
10
11
12
13
14
15
16
17
18
19
14
10
7
5
3
2
8
5
4
3
6
7
0
5
2
4
4
5
2
4
2
3
1
1
2
0
5
3
4
3
2
4
0
4
4
7
17
15
13
10
19
28
18
20
Table F.2.
Case
Number
1
1
2
4
5
6
1
12
6
6
Raw task data for NLD group.
2
3
4
5
6
7
8
2
1
6
5
2
3
6
4
2
5
1
2
2
3
2
0
4
2
*)
0
2
0
2
0
1
2
0
0
0
1
0
0
1
0
1
0
31
32
17
30
25
29
23
18
32
26
27
24
27
28
26
32
27
32
5
7
1
1
1
3
4
1
5
2
5
5
1
3
9
1
4
5
3
i
30
31
10
30
23
28
22
17
31
23
27
21
27
26
26
32
26
31
30
21
3
1
2
1
4
2
1
2
5
6
28
27
17
31
27
28
31
29
17
20
17
18
21
19
19
14
18
22
19
21
16
19
18
19
23
22
22
19
17
19
18
19
15
20
17
19
20
20
18
1
3
3
3
2
4
5
4
2
3
6
5
1
2
2
1
5
2
3
5
4
1
1
3
4
1
3
4
2
6
7
i*
6
9
10
11
12
13
14
15
16
17
18
20
9
7
2
6
2
4
3
6
4
1
6
2
:i
r^
j
%
2
fr
fr
0
(1
30
31
4
1
3
3
2
3
2
5
3
5
3
0
29
0
0
0
0
1
1
0
1
3
1
29
27
21
32
27
28
31
29
23
24
:s
26
27
28
29
30
31
32
2
3
1
2
1
4
3
3
28
Variable
9
10
46
41
40
41
43
38
45
39
44
42
43
42
45
41
43
46
43
44
45
40
38
46
45
44
43
47
46
42
41
40
24
15
18
17
17
13
12
9
15
15
19
14
16
18
20
19
11
15
12
11
13
18
16
18
16
20
21
20
16
12
11
12
13
14
15
16
17
18
0
5
0
2
4
7
4
7
2
2
3
5
2
1
2
2
3
2
4
1
7
0
2
3
3
1
0
2
0
8
0
0
2
4
0
3
4
6
3
3
2
0
C
5
0
0
5
3
4
3
3
2
0
1
4
0
2
0
5
0
0
1
2
0
2
1
4
2
2
1
1
3
0
0
1
0
2
2
2
4
1
O
1
4
3
2
2
1
1
1
3
4
0
3
7
1
2
4
4
3
3
6
1
3
7
2
0
4
2
3
2
3
0
1
5
4
1
2
1
1
2
1
0
3
0
0
1
3
1
2
1
2
2
0
0
0
0
1
0
0
0
0
0
0
7
2
2
5
4
5
3
1
2
2
0
2
1
0
5
3
3
0
5
0
0
0
0
0
0
0
0
1
0
0
1
2
1
1
2
3
1
4
1
4
0
1
0
0
3
1
6
2
1
0
0
1
1
1
0
1
3
2
0
3
8
2
4
2
3
5
1
2
2
4
0
3
3
1
2
1
3
2
2
0
0
1
3
0
0
0
0
5
0
1
2
0
0
0
2
2
19
25
21
4
15
17
15
15
11
18
17
20
12
25
19
20
21
14
18
12
19
15
25
25
23
21
23
25
24
H
22 U>
[S3
17
Table F.2.
Raw task data for NLD group—Continued.
Case
Number
1
2
3
4
5
6
7
8
33
34
35
36
0
7
7
4
0
4
2
4
1
0
0
0
29
25
24
17
2
7
4
3
28
19
21
15
18
17
18
18
3
4
3
5
Variable
9
10
11
12
13
14
15
16
17
18
19
18
13
20
11
2
8
1
2
2
1
1
3
0
1
0
2
3
2
3
7
0
3
2
2
0
3
0
0
0
2
0
0
1
5
0
6
24
12
23
17
A3
40
43
44
APPENDIX G
d' VALUES FOR TASKS THREE
AND FOUR:
SPELLING
Appendix G presents d' values for Task Three: Spelling (Yes-No)
and Task Four:
Spelling (2AFC) for the research groups.
The learning
disability group is denoted by case numbers 37 through 72; the nonlearning disability group is denoted by case numbers one through 36.
134
135
Table 6.1.
6ase
Number
37
38
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
65
66
67
68
69
70
71
72
d' values for Tasks Three and Four:
LD
Yes-No
0
-.20
-.62
.40
.76
0
.21
.30
-.18
.32
-.32
.31
.41
-.94
.69
.63
-.83
.96
0
.21
.63
.94
.20
.53
-.31
-.45
.22
.94
.76
0
.10
-.30
-.20
0
2AFC
Case
Number
.90
-.14
-.14
.66
0
.90
.28
.74
-.14
.21
.60
.51
.36
-.74
.74
0
.43
.74
.66
.21
-.07
.60
.36
-.60
-.14
0
.43
.66
0
-.60
-.43
.21
-.51
-.36
1
2
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
Spelling.
NLD
Yes-No
2.59
.86
1.76
2.16
2.10
1.70
.99
1.57
2.58
1.88
1.70
1.20
2.46
1.98
2.10
3.15
2.02
2.58
1.57
1.31
1.70
2.33
2.46
1.43
1.83
2.22
1.88
1.88
2.24
1.2a
1.76
1. 52
1.76
1.42
2AFC
1.98
1.29
1.19
1.29
1.53
1.00
1.81
1.09
1.66
1.40
1.53
1.40
1.81
1.29
1.53
1.98
1.53
1.66
1.81
1.19
1.00
1.98
1.81
1.66
1.53
2.19
1.98
1.40
1.29
1.19
1.53
1.19
1.53
1. 66
APPENDIX H
p(e) VALUES FOR TASK THREE:
SPELLING (YES-NO)
Appendix H presents p(e) values for Task Three: Spelling
(Yes-No) for the research groups.
The learning disability group is
denoted by case numbers 37 througli 72; the non-learning disability
group is denoted by case numbers one through 30.
137
p(e) values for Task Three: Spelling (Yes-No) for the
learning disability and non-learning disability groups.
LD
p(e)
37
38
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
W
59
60
61
62
63
65
66
67
6«
69
70
71
72
.44
.48
.44
.48
.38
.48
.40
.50
.48
.34
.34
.42
.44
.32
.32
.40
.48
.42
.48
.40
.40
.46
.44
.38
.42
. 32
.36
.46
. 38
.4S
. 38
. *6
.52
.40
Case
Number
1
2
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
20
21
22
23
24
25
26
27
28
29
30
31
3.'
J)
34
35
36
NLD
p(e)
.42
.40
.42
.48
.42
.46
.38
.44
.48
.44
.54
.42
.40
.40
.42
.48
.54
.48
.44
.44
.46
.38
.40
.36
.48
.36
.44
.48
.44
.48
.42
.43
.42
.46
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